Home Secretary Theresa May is due to hold talks in Paris amid the deepening crisis of migrants camped in Calais looking to cross the Channel to Britain.
Ms May will meet her French counterpart Bernard Cazeneuve as cross-Channel chaos sparked by striking ferry workers continues to disrupt sailings from Dover.
Thousands of lorry drivers are parked on the M20 in Kent for a fourth day as the partial closure of the Port of Calais has crippled Channel crossings.
Migrants camped near the French port have been taking advantage of slow-moving and queueing traffic by trying to board UK-bound vehicles.
Port of Dover officials said this morning they had no idea when the industrial action - the second strike by ferry workers in a week - would end.
There have been calls from the UK's Road Haulage Association for the military to be deployed to break the strike as livelihoods and lives were at risk.
Its chief executive Richard Burnett said it was "absolute mayhem", adding: "The time for talking around the table has passed.
"The UK and French governments must acknowledge their responsibilities to all Port of Calais users, move in and act. If this means deployment of the armed forces then so be it.
"Let's get this desperate mess sorted out now and talk about a long-term solution afterwards. The scale of the current situation has to be seen to be believed.
"The only word to describe what is happening there is absolute mayhem."
The disruption began on Monday when MyFerryLink workers staged a wildcat strike in protest at expected job cuts in the French port city.
The blockade at Calais was partially lifted at 6pm yesterday, allowing P&O to commence a "limited" service.
But with only one sailing at a time allowed to enter the port, ferry services continue to be badly affected. The Channel Tunnel reopened on Tuesday afternoon following a three-hour shutdown.
Food and water were distributed throughout yesterday to stranded drivers forced to park on the M20.
Kent Police have implemented Phase 4 of Operation Stack, where freight traffic is held on the coastbound carriageway of the M20.
More than 3,000 people displaced from countries including Eritrea, Syria and Afghanistan have set up camp around Calais.
Meanwhile, P&O Ferries chief executive Helen Deeble hit out about the ferry disruptions caused by the strike, with fierce criticism of the British and French governments as well as Eurotunnel.
She pointed out that P&O Ferries employs thousands of people on both sides of the Channel and "this damaging and dangerous industrial action is now putting those jobs at risk".
Crew members and catering staff on MyFerryLink services announced the strike after Eurotunnel, which owns the ships, sold the cross-channel service to rival operator DFDS.
The sale came after a competition authority ruling and left up to 600 jobs, including 70 in Dover, under threat.
Kent County Council said its staff provided 2,000 bottles of water and 750 snack meals on Tuesday, and a further 5,000 bottles, plus 200 meals, were expected to have been distributed yesterday to drivers caught up in Operation Stack.
The Maritime and Coastguard Agency, Kent Police and Kent Fire and Rescue Service were helping hand out the drinks and food along the closed stretch of the M20.
Motorists were told to avoid the area and some vented their frustration about the delays caused by the strike on the other side of the Channel.
On Twitter, one wrote: "This Operation Stack is a disgrace, wasn't even travelling in the direction of France and it's still causing hour delays."
Another tweeted Conservative Dover MP Charlie Elphicke, saying: "For the record, the people of Dover are now stranded, completely cut off in their own town."
Cabinet minister Oliver Letwin chaired a meeting of the Government's Cobra emergency committee to discuss the situation in Calais, and Prime Minister David Cameron spoke by phone with French president Francois Hollande.
Mr Cameron spoke to Mr Hollande for about 10 minutes shortly before taking questions from MPs in the House of Commons yesterday.
The PM's spokeswoman said Mr Cameron welcomed the co-operation Britain had received from the French authorities and said it was important to get the port open again and to ensure the Channel Tunnel remains open.
Mr Hollande responded that he was determined to resolve the situation and welcomed the fact that the UK and France were working together on the issue.