Eurotunnel says it is preparing for a “difficult night” and has increased security after 150 migrants tried to storm the Calais terminal.
Services were disrupted after migrants accessed restricted areas on Saturday.
Keith Vaz, chairman of the Home Affairs Select Committee said the EU must tackle the “problems of people arriving in the EU itself”.
Calais’s deputy mayor, Philippe Mignonet, wants the UK to introduce ID cards and employment controls.
Freight services are also delayed, Eurotunnel said, and freight lorries queued on the M20 in Kent for the second time this week.
Mr Vaz, who met Mr Mignonet in Calais to discuss the problem, said a solution to the migrant issue must be collaborative.
“This situation is only going to get much worse, until the EU takes a grip of the problems of people arriving in the EU itself. That means the southern borders, and the border between Greece and Turkey.
“We just need to do this, in a very clear way, say to the EU this is an EU problem. Secondly we need to tackle the criminal gangs.”
Mr Mignonet said the UK could do more to deter migrants.
“We know in England there are no identity cards for example, nor identity controls, nor controls in companies to fight against illegal workers.” he said.
“That’s a first step. When people will know that they can’t work easily in England on the black market, they will change their mind.”
Migrants entered restricted areas on the French side overnight on Friday, delaying and cancelling services, Eurotunnel said.
A spokesman for the company called for “immediate action” from authorities to protect the tunnel and provide a solution to the migrant crisis.
He also said there had been “huge numbers of migrants” in and around the area on Friday night.
Le Shuttle passengers, who are facing delays, are still being encouraged to check-in on time.
As a result of disruption, Kent Police initiated phase two of Operation Stack – where freight traffic is parked on sections of the M20 motorway on the English side of the Channel – but this was lifted on Friday afternoon and the road is now fully open.
The Fresh Produce Consortium estimates that £10m of fresh fruit and vegetables have been thrown away since the start of the year, as a result of the problems in Calais, which have included technical issues in the Channel Tunnel and strike action by ferry workers in France.
Dan Cook, operations director at Europa Worldwide, a transport and logistics business, said “marauding mobs” of migrants were breaking into the company’s vehicles.
Mr Cook said: “This isn’t in lay-bys off the beaten track at night, this is in broad daylight on the motorways approaching Calais and what you see, to be blunt, is marauding mobs around trailers… climbing on board, breaking open backdoors with broadly no sign of any sort of policing to prevent it.
“If we were watching television in the UK and we were seeing mass groups of people wandering around the motorway climbing on vehicles I think we would be pretty outraged and we would expect the British authorities to do something about it.”
Are you in Calais? Did you witness what happened? Are you still in the area? Emailwith your experiences.
If you would be happy to speak further to a BBC journalist, please include a contact telephone number. You can also tweet your stories to @BBC_HaveYourSay or text 61124. If you are outside the UK, send them to the international number +44 7624 800 100.
Or WhatsApp us on +44 7525 900971
Read our terms and conditions.