The British and French governments have pledged to increase security at the Eurotunnel after one migrant died during an attempt by hundreds to storm the Channel Tunnel.
Eurotunnel has revealed that since the beginning of the year it has blocked 37,000 migrants trying to make their way to Britain, and that in the last month nine people have died trying to cross the Channel.
The operator said that on Monday night 2,000 attempts were made by people to storm the tunnel, and that it had fielded 1,500 more last night - when a man believed to be a Sudanese national was crushed under a truck.
Although no one succeeded last night, it is thought that up to 148 people made it to the UK after Monday's incursion.
French police have been urged to take a "zero tolerance" approach to the crisis or face British deportation centres being "overwhelmed" with migrants.
Home Secretary Theresa May confirmed that "a number" of people crossed the border, adding that the French and British governments needed to work with Eurotunnel to quickly address the issue.
Speaking at the Home Office, Mrs May 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."
However, a spokesman for Groupe Eurotunnel, which manages and operates the Channel Tunnel, said that since the arrival of migrants in the area around Calais, it has invested more than 160 million euro (£113 million), including 13 million euro (£9.2 million) in the first six months of 2015, in physical resources - fences, cameras, infra-red detectors - and personnel.
He added: "These considerable investments have already been followed in the second half of the year with new fencing around the platforms. Security patrol staff has been doubled to reach 200 employees, including sniffer dog patrols."
The spokesman also said that Eurotunnel has kept the Intergovernmental Commission for the Channel Tunnel and authorities informed, over several months, about the "explosion" in the number of migrants present in Calais.
"The continuous pressure exerted every night is above and beyond that which a concessionaire can reasonably handle and requires a constructive and appropriate response from the governments," he added.
Speaking after chairing a Cobra meeting, Mrs May said the Government was pressing for rapid installation of the new security fencing at Coquelles.
When asked if the military should be used, she replied: "This is about ensuring we get that security fencing up, it's about working with Eurotunnel to ensure we have got the best measures in place."
French interior minister Bernard Cazeneuve announced that France would be temporarily deploying two mobile units, or 120 additional police staff, in Calais "in order to contribute to the security of the site".
He also called on Eurotunnel to address security issues, adding: "In Calais, the state hasn't stopped assuming its responsibilities of maintaining public order, dismantling (immigration) networks, keeping foreigners without papers away, and putting into place humanitarian solutions for migrants and asylum seekers.
"Eurotunnel needs to also assume its responsibilities, notably regarding security."
Labour MP Keith Vaz, who chairs the Home Affairs Select Committee, said he had witnessed 148 migrants successfully make the journey illegally to England yesterday morning while at an immigration processing centre in Folkestone, Kent.
Mr Vaz said: "The committee warned before the summer recess that the situation in Calais would descend into a summer crisis.
"David Cameron needs to meet Francois Hollande as soon as he returns. This can only be dealt with at the highest levels.
"The French police need to show zero tolerance and end the daily onslaught of thousands of people trying to board the freight trains. The police and services in Kent will soon be overwhelmed unless drastic action is taken.
"The committee will consider whether to conduct another report into this matter when it returns after the recess."
The crisis has caused travel chaos on both sides of the Channel, with motorists reporting long queues to get into the terminals.
Kent Police said Operation Stack - where freight traffic is parked on the M20 when cross-Channel crossings are disrupted - is expected to last into the weekend.
Sailings from the Port of Dover continued, with P&O Ferries running full services to Calais and DFDS operating a full schedule to Dunkirk and Calais.