Migrants in Calais have been filmed scaling a 5m high (16ft) security fence, giving them access to lorries already through customs.
The security breaches, occurring day and night, were filmed by the BBC.
Those who were caught were immediately released by the French authorities.
Home Affairs Select Committee chairman Keith Vaz said the French were not doing enough to address the problem, but the Mayor of Calais had previously said Britain should help more.
After watching BBC South East Today's footage, Mr Vaz said: "I'm astonished that the French authorities are not cooperating with us in preventing people putting their lives at risk on a daily basis in trying to get to the UK.
In March, migrants were filmed sitting on the axle's of lorries in a desperate attempt to cross the Channel.
A Border Force spokesman said: "We have already made improvements to security at Calais, working with the French authorities.
"We have, for instance, upgraded vehicle scanning equipment with the latest technology to detect people hiding in lorries and tankers and have increased the number of body detection dogs stationed at Calais."
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