William Hughes, the codebreaker's uncle, said Mr Williams' parents Ellen and Ian were 'furious' at suggestions their son has been labelled as gay and a cross dresser.
'It is completely false,' Mr Hughes, 62, who yesterday visited the Williams's family home in Holyhead, North Wales.
'They are very, very angry,' he told the London Evening Standard.
'The lad had been away from home for a long time — we did not know much about his private life, but it has never crossed any of our minds that he could be gay.
'It's not the picture they have of their son.
'Maybe it's the Government or somebody trying to discredit him.'
The mathematics genius, who was on secondment to MI6, was found dead in a sports holdall in the bath of his Government flat on Monday.
Scotland Yard detectives continued to investigate whether GCHQ codes expert the 31-year-old lived a secretive double life.
Police sources believe one theory is the spy's killer may have planted a trail of clues to make it seem as though he was murdered by a gay lover.
They said gay magazines and the phone numbers of gay escort men were found in the apartment near the agent's body.
The latest reports on Mr Williams include claims that bondage gear and equipment associated with sado-masochism had been discovered in the flat he used in Pimlico, London, while it has also been claimed he had links to a male escort.
Mr Williams lived alone and did not have a partner.
But people who knew the cycling enthusiast said he never gave any indication of being homosexual and a former landlord, who rented a flat to him for ten years, never saw him bring anyone – male or female – back to his home.
Sources close to the inquiry have dismissed some of the allegations, which raises questions over who was behind them - and why they were made.
'Dirty tricks': William Hughes, Gareth's uncle, said today his Holyhead-based parents fear Mr Williams is the victim of a government smear campaign
Mr Hughes, a cousin of Mr Williams's mother, Ellen, said: 'I have spoken to Gareth's parents and they are not doing well at all.
'They are in a state of shock and struggling to come to terms with what has happened.
'They have seen what has been in the papers and they are very, very upset about these untruths. I don't see any evidence of it.
'It never crossed my mind that Gareth was that sort of person. He left home at a young age and what happened in his private life was his business,' he said.
'When you have these rumours in the papers, it is most distressing.
'It is heartbreaking that he has died so young and his family have enough on their plate without having to read these stories.'
spokesman for the Foreign Office said: 'There is no question of there
being a government dirty tricks campaign; we are as concerned as the
family to establish the facts of Gareth's death.
'But the police investigation is now underway and we must await its outcome.'
The family criticisms comes as CIA agents began examining details of Mr Williams's work and private life in the US to establish if there could be a link to his death — or a threat to national security.
The Daily Mail can reveal Mr Williams flew to the National Security
Agency, the Pentagon's listening post and the largest intelligence
agency in the world, up to four times a year.
National Security Agency: The largest intelligence agency in the world, bases at Fort Meade, Maryland. It is understood that Gareth Williams visited the facility up to four times a year
Mr Williams, who worked for the GCHQ listening station in Cheltenham but was on secondment to MI6 in London, returned from his last trip to America only a few weeks before he was found dead.
Questions also remain over why his body lay undiscovered for up to a fortnight at his £400,000 flat in a Victorian townhouse in central London, half a mile from MI6 headquarters.
The body of the keen cyclist was found in a sports holdall in the bath on Monday afternoon.
But yesterday his former landlady in Cheltenham insisted he had not been off work, intensifying the mystery surrounding his death.
sources could not explain why some one holding such a sensitive post
was able to go 'missing' for such a long time before police were
Officers were last night examining the hard drive of a laptop computer found
in the flat.
Landlady Jenny Elliott said: 'He definitely wasn't on annual leave as the security services woman who came to see me after they found his body told me that he wasn't on holiday.
On guard: A police support officer guards Mr Williams former home. The CIA have now joined the investigation into his death, although there is said to be 'no panic' that his death may be related to his intelligence work
'Why did no one notice? It's disgraceful the police weren't alerted earlier that he was missing. His murder is devastating and I just hope the person who did it is caught.
Mrs Elliott, 71, who rented Mr Williams a self-contained flat attached to her home in Cheltenham, said he would often travel to America for weeks at a time three or four times a year either with a male colleague or on his own.
His uncle, Mr Hughes, who lives in Anglesey, North Wales where Mr Williams grew up, said: 'He'd been making the trips for a couple of years.
'I only found this out very recently and I do not know where in America he was staying or who he was working for out there, but I do know it was in relation to his job.
'His last trip was this summer. He returned from the States just a couple of weeks or so before he died.'
A U.S. intelligence source said there was 'no panic' yet within the National
Security Agency and people who knew Mr Williams were still to be questioned.
The source said: 'The strong implication is that his death is not connected
to his intelligence work, though this could change at any time. They are understandably concerned about what has happened and are keeping a close eye on developments.'
Police are still waiting for the results of toxicology tests which could shed
light on how he died.
Police have also asked a pathologist to check whether Mr Williams's neck was broken, which would suggest a professional hit, the sources said
A postmortem examination proved inconclusive and now they must wait for toxicology results to find out whether drugs, alcohol, poisoning or suffocation were the cause of death.
Sources say he was not stabbed, shot, strangled or beaten. Scotland Yard is describing the death as 'suspicious and unexplained'.
A former MI6 officer said that intelligence chiefs are furious that details of Mr Williams's work as a spy had been leaked.
Harry Ferguson said senior officials at the Secret Intelligence Service wanted to suppress any information about his work and to simply refer to him as a 'civil servant' when news of the murder was made public.
'They hoped details of his role could all be kept covered up. It is a standard
process. Blurting it out has caused a lot of unnecessary embarrassment, risk and upheaval to the SIS.
'If it had been managed properly it could have been kept quiet. He could simply have been described as a government worker or civil servant.
'They are especially frustrated that it has emerged that not only was he was working in GCHQ, but also on secondment to MI6.'
Mr Ferguson said secret service bosses feared that the 'nightmare scenario' had come true when the body was discovered.
'One of the concerns about having such a high profile building as the SIS does is that, while staff can be protected when inside the building, there a significant risk that they could be followed home,' he said.
'It is the sort of thing that a small group of Islamists or other terror network would clearly be capable of doing.'
He said the apparent 'ritualistic' scene at Mr Williams' flat, with his mobile phone and SIM cards carefully laid out, also suggested it could have been carried out by a foreign agency to send a message.The reclusive maths genius and rumours of cross-dressing and blackmail
From a tender age, it was clear to his teachers at Morswyn primary school on Anglesey that there was something special about Gareth Williams.
A talented pupil, he was fast-tracked through education, earning his maths GCSE aged nine while most of his contemporaries were still grappling with basic arithmetic.
By 13 he had secured his A-levels and had a degree in maths by 17.
He was known as ‘the maths genius’ by fellow pupils and possessed the ‘fastest brain’ his teachers had encountered. But his academic excellence came at a price.
Bright boy: Gareth Williams, centre, with classmates in 1987. He staggered teachers with his ability in maths, passing a GCSE aged only nine, and obtaining his A-Level at 13
Forced to study with children several years older than himself, he found it hard to make friends and was last night described by former school mates as ‘socially naive’ and ‘introverted’.
Detectives were last night investigating whether this shy, private side to his nature made him vulnerable to blackmail amid lurid claims that he was a secret cross-dresser.
Geraint Williams, his maths teacher at secondary school, recalled how young Gareth was so clever that he sat his intermediate maths GCSE, gaining a grade B, while still at primary school, before being moved up to Bodedern Secondary School, Holyhead, a year ahead of his peers.
Within months of his arrival he took his advanced GCSE, scoring an A grade, and received top marks in A-level maths and computer studies two years later, when he was 13.
His teachers were initially at a loss at how best to educate him.Their solution was to move him up two years and enrol the youngster, then aged15, on a three-year maths degree course at his local university at Bangor, which heattained in just two years with first class honours.
Teacher Mr Williams said: ‘I’d heard about this amazing pupil who had done his GCSE at primary school and got a B at intermediate level.
‘He took the higher level GCSE in a couple of months and got an A. It was a problem for us – what could we do with him? We got him to follow A-levels and he did A-level maths and computer science in the third-form. He achieved As in them.
‘That was a big problem because he was still only 13, so we contacted Bangor University and he followed the first year of maths degree course.’
The teacher added: ‘He was the best logician and the pupil with the fastest brain I have ever met. You only had to say things once, that’s why he was so successful. He could understand things immediately. He was also extremely good with computer science.
‘Gareth was also a very nice lad, quiet and unassuming. It’s very sad.’
After leaving Bangor University at 17, Mr Williams went on to study for a PhD at Manchester University before enrolling in postgraduate certificate at St Catharine’s College, Cambridge, in 2000.
He dropped out a year later, but last night friends speculated that he left afterbeing taken on by the Secret Services, which traditionally recruit from Oxbridge.
They said it was an open secret that Mr Williams worked at GCHQ, but added that any notion that the quiet, unassuming boy lead a James Bond spy lifestyle was laughable.
One close friend, who attended primary school with Mr Williams, said: ‘Gareth was a super, super brain. Beyond intelligent, a very, very clever guy.
‘He was hand-picked while at Cambridge by the services, they want the cream of the crop and he certainly was that.
‘It was common knowledge that he worked at GCHQ, but any notion that he led a James Bond style lifestyle is rubbish.
‘Those kind of people have to be able to blend in, but Gareth wasn’t like that, he was very different.
‘He was introverted and found it difficult to make friends, but he was a lovely, lovely bloke. It is such a tragic waste of such a talented life.’
The family home: Mr Williams was raised in Holyhead by parents Ian and Ellen. Last night they were said to be 'devastated' at the death of their son
The dead man’s parents, Ian, an engineer at Wylfa power station, and mother Ellen, who worked in education, were on holiday in America celebrating their joint 50th birthdays when news of their son’s death broke.Last night they were said to be ‘devastated’.
Another former school friend, Dylan Parry, 34, said he was ‘dumfounded’ by the murder.
‘Gareth was the last person I would have believed would be involved in the murkier elements of life,’ said Mr Parry, of Holyhead. ‘He really was about as far from a James Bond figure as it’s possible to imagine.
‘Gareth was introverted and socially awkward. He wasn’t dashing or cavalier or a charmer, although he was extremely nice in a quiet way.
‘There has been a lot of speculation about his sexuality, but he was so introverted as to be asexual.‘
He wasn’t able to form relationships because he was so obsessed with his maths studies.
‘We nicknamed him the maths genius because he was so clever. He was so naive, he was someone people could easily take advantage of.
‘I wouldn’t have thought he was a very good judge of character and it’s possible he got to know someone who wasn’t very safe. He was so innocent.’