Eurotunnel, the company operating the tunnel between France and England, says it has blocked more than 37,000 migrants trying to cross illegally from continental Europe to Britain since the beginning of the year.

Eurotunnel announced the total Wednesday, saying France and Britain need to do more to help Eurotunnel cope with the rising numbers of migrants flooding into the area.

The announcement comes after two nights of record numbers of migrants trying to enter the tunnel.

Authorities in the northern French port city of Calais said Wednesday that during the overnight hours they counted another 1,500 migrants who have tried to enter the Eurotunnel in hopes of reaching Britain, finding the body of at least one who failed at the attempt. That followed a record total on Monday night, when police pushed back more than 2,000 migrants.

The person who died is reported by France Info website to have been a Sudanese man aged 25 to 30 years who may have been hit by a truck.

British Prime Minister David Cameron, who is currently in Singapore, said on Wednesday that Britain is doing everything it can, cooperating with France, to prevent disturbances as the Eurotunnel site, where migrants have been gathering over the past six weeks to try to make their way from France to Britain. Eight migrant deaths have been reported at the tunnel since mid-June.

As many as 10,000 migrants from Africa, the Middle East and beyond are living in squalid encampments in and near Calais, a city of 70,000.  Observers say their push to enter the 50-kilometer undersea tunnel has intensified in recent weeks, after authorities stepped up port security to block migrants from stowing away on Britain-bound vessels.

Monday's tunnel confrontation caused major delays in Eurotunnel service for much of Tuesday.

Eurotunnel train service and vehicle traffic also was suspended overnight Saturday into Sunday, in a similar confrontation between migrants and police.