Border security is being stepped up in northern France and Dover after migrants sought to exploit ferry strike action in Calais.
Hundreds of migrants at the French port tried to board vehicles heading to the UK on Tuesday.
Immigration minister James Brokenshire told the BBC that the situation was “hugely regrettable”.
But he said it was “ultimately” up to the French authorities to “assure security and safety” at Calais.
Industrial action by French ferry workers forced the suspension of services through the Channel Tunnel between the UK and France on Tuesday.
Hundreds of migrants tried to board slow-moving UK-bound lorries amid the chaos.
About 3,000 migrants are estimated to be living rough around Calais, waiting for a chance to cross the Channel.
Mr Brokenshire, a Home Office minister, told the BBC: “It is hugely regrettable that we’ve seen these incidents occurring as a result of industrial action in France.
“We are putting additional resourcing into the port of Dover to enhance screenings and detections there so that we’re looking at this on both sides of the Channel.”
He added: “We have been advised the French authorities are sending further policing to deal with law and order issues, and we will be keeping in close contact with them in the hours ahead.”
Last year, the UK government pledged £12m to help France tackle the problem of illegal immigrants trying to enter Britain through Calais.
Mr Brokenshire said he had been giving advice to drivers through the Road Haulage Association and the Freight Transport Association.
“These deployments of additional border force resourcing at Coquelles around the Eurotunnel terminal and also from our work at Calais, buttressed by further support at Dover, is about maintaining that safety and security and the integrity of the border, which is our absolute focus,” he said.
The Home Office says about 19,000 attempts to cross the Channel have been prevented so far this year, more than double the number during the same period last year.
Keith Vaz, Labour chairman of the Commons Home Affairs Committee, told the BBC that the migrant situation was the “biggest crisis” facing Europe.
He said migrants were trying to reach the UK because “it’s the country they think they can work in illegally”.
But he argued that more needed to be done across Europe to tackle the problem, saying it was “too late” to wait until they arrived at Calais.
The deputy mayor of Calais has blamed the UK for the migrant surge – and said the British government should be doing more to address the problem.
But Conservative Craig Mackinlay, South Thanet MP, said the problem “lies elsewhere, and that’s at the heart of the ports in Libya where this trafficking is actually starting”.
He said the government was “doing our bit” to stabilise such countries, but he told the BBC the migrants had passed through many European countries before arriving at Calais.
“It’s not our problem,” he said.
“It’s unfair, it’s unacceptable and it’s not going to happen that it becomes Britain’s problem.”