A man has been killed as at least 1,500 migrants tried to enter the Channel Tunnel in Calais during Tuesday night, French police have said.
Eurotunnel, which says incursions are now a nightly occurrence, said migrants had been removed from the site. It advised freight services to consider alternative transport for Wednesday.
Sections of the M20 in Kent are closed in both directions for Operation Stack.
It comes as the UK government comes under pressure to combat the crisis.
Speaking after a meeting of the government's emergency Cobra committee, Home Secretary Theresa May said the UK was pressing for the rapid installation of 1.2 miles of new security fencing which it has pledged to pay for at Coquelles, near the tunnel entrance.
Mrs May added there were some migrants "particularly trying to get into the Eurotunnel and on to the trains before that security fencing is going up".
France's interior minister said 120 police officers were being sent to Calais to reinforce security at the site.
The man who died is described as Sudanese, aged between 25 and 30.
French police said he was probably crushed by a lorry which was exiting one of the shuttles that transport vehicles through the tunnel.
He is the ninth person to die trying to access the tunnel since June.
- M20 closed London-bound from J9 to J8 and closed coast-bound from J8 to J11
- Eurotunnel says its passenger services are running, with a delay of two hours on the UK side and one hour on the French side
- Freight services face a one-hour delay before check-in on the UK side; with an estimated more than six-hour wait to check-in in France
- P&O ferries and DFDS Seaways say all their services are operating to schedule between Dover and Calais
Eurotunnel said some 2,000 migrants had tried to get into the terminal on Monday.
A spokesman said it was an issue for the government to "sort out", adding. "We need them to stop the migrant flow from Calais but it appears to be too much for them to handle."
Mrs May said some migrants had reached Britain through the Channel Tunnel, but did not say how many had arrived.
Speaking after Wednesday's Cobra meeting, she said: "Crucially what we are looking at now is improving security at the railhead at Coquelles, so we can ensure people are not trying to come through the tunnel.
"That means some urgent work in government but also with Eurotunnel, and Eurotunnel has a role to play here in the measures they themselves put in place to protect their trains."
The Home Office has pledged to spend £7m on 1.2 miles of fencing there.
'Drunk with tiredness'
Lorry driver Sean Swan took 23 hours to travel from the M20 to Calais on Tuesday and said he only got through because he was carrying live fish.
"I was given a police escort from Junction 8 all the way to Dover, even after making the officer aware that it was now illegal for me to drive.
"We bypassed thousands of stranded lorries. At one stage I felt drunk with tiredness at the wheel of a 44 tonne machine."
He said in the past month, migrants had managed to board the train on every journey he made from France to Britain.
Drivers found with migrants hiding on their vehicles can be fined but many are afraid to challenge them.
"They are jemmying the padlocks off, with hammers, crowbars and Stanley knives.
"On one side you risk your life and on the other you risk your livelihood."
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'Get a grip'
Speaking from Singapore, PM David Cameron said: "I have every sympathy with holidaymakers who are finding access to Calais difficult because of the disturbances there and we will do everything we can to work with the French to bring these things to a conclusion.
"There's no point trying to point fingers of blame - it's about working with the French, putting in place these additional security measures, adding in the investment where that's needed. Britain will always come forward with that."
But Labour's interim leader, Harriet Harman, urged the government to "get a grip" as the Calais situation caused a "major problem" for Kent.
She said diplomacy with the French had not worked, adding: "What the government should be doing is getting the French to sort out the people who are all massed at Calais to discover - are these people genuine refugees who the French should give asylum to, or are they people who the French need to be deporting?"
Meanwhile, Kent Police has reintroduced Operation Stack, leading to long delays for lorries on sections of the M20 near the Channel Tunnel.
Richard Burnett, chief executive of the Road Haulage Association, which represents lorry drivers, repeated a call for the French military to "contain, segregate and control the situation".
And UKIP leader Nigel Farage said the port of Calais had become "virtually lawless", fearing that "unless something radical is done it is only a matter of time before a British holidaymaker or lorry driver dies".
He told the BBC's Victoria Derbyshire programme he was surprised the French had not brought in their army to help with the crisis.
The home secretary held talks on the migrant issue with French Interior Minister Bernard Cazeneuve on Tuesday, saying the two governments were working "in close collaboration and co-operation".
An official count at the beginning of July found about 3,000 migrants - mainly from Ethiopia, Eritrea, Sudan and Afghanistan - were camping in Calais and trying to get across the Channel, AFP reported.