Members of the royal family are regularly accompanied by police guards in their day to day activities and there are records of where and when the officers were sent—or at the very least a record of which officers worked on which day. If these records were to be made available investigators could easily determine where Prince Andrew was on the night in question, but police are saying that handing over such information could pose a threat to national security.
During his disastrous BBC interview, Andrew claimed that he was at a Pizza Express in Woking on the night then 17-year-old Giuffre (nee Roberts) says the pair visited a club and later had sex. If the Duke is indeed telling the truth, then his claims could be very easily corroborated by whichever guard was on duty at the time.
Unfortunately, Scotland Yard has not been willing to cooperate.
In a statement responding to the inquiry, Scotland Yard said that revealing information about the disgraced prince's whereabouts on the night in question could "undermine the safeguarding of national security," according to the Sun.