The keen amateur cyclist, from Croydon, was peddling at around 35mph as he sprinted to the finish line in the town of Marigny in Normandy.
The 27-year-old driver of a van, which was supporting one of the other teams, was taken to hospital suffering from shock, while attempts to revive Mr Bashford failed.
It is understood the van driver was from Guernsey in the Channel Islands.
Mr Bashford was a retired Metropolitan Police officer whose job involved protecting high profile politicians, including Tony Blair.
He was a member of the Old Portlians Cycling Club, which was founded in 1921 as a club for former pupils of Portland Road School in south east London.