The five people managed to scramble aboard the vehicles in Calais as they made their way back from the Monaco Grand Prix carrying broadcasting equipment.
But the group, believed to be from Eritrea, were out of luck when staff at billionaire Ecclestone's Formula One Management company contacted police when they discovered the stowaways while unloading at the firm's HQ in Kent.
The UK Border Agency confirmed that the immigrants were arrested at Biggin Hill Airport, FOM's base of operations, and are currently having their asylum claims processed.
A company spokesman was shocked, and claimed that F1 trucks had never previously been used by people trying to enter Britain undetected.
"This is the first time we have had such a problem," the spokesman said.