Extra security guards have been stationed at Calais to try to tackle the migrant crisis while David Cameron faces calls to break his holiday and witness its impact "first-hand".
Shadow justice secretary Lord Falconer will visit the French port to discuss the situation with Eurotunnel officials and the Road Haulage Association (RHA).
A Labour spokesman said: "No UK Government minister has visited the Eurotunnel railhead to see first-hand the problems faced by the rail operator because of the failure to get to grips with migrants in northern France."
The RHA urged Mr Cameron to visit Calais and see what lorry drivers are experiencing, as pressure mounts on the Government to secure a long-term solution to the crisis.
RHA chief executive Richard Burnett said: "Without witnessing the mayhem at Calais first-hand, neither the Prime Minister nor his advisers can fully grasp the severity of the situation.
"I have therefore issued an invitation to David Cameron to travel with him across the Channel to see for himself the appalling conditions that drivers are facing."
Lorries have repeatedly been targeted by migrants desperately trying to reach Britain.
The crisis is said to have cost the economy millions of pounds as hauliers are forced to dispose of contaminated goods and wait in lengthy queues on the M20 in Kent.
Foreign Secretary Philip Hammond insisted the Government has the crisis in hand and said 100 additional guards are on duty at the terminal.
He said: "I think we have got a grip on the crisis. We saw a peak last week, since when the number of illegal migrants has tailed off.
"We have taken a number of measures in collaboration with the French authorities and Eurotunnel which are already having an effect and over the next day or two I would expect to have an even greater effect."
Mr Hammond did not directly address Mr Cameron's absence, due to end on Thursday before he takes further time away from the office.
Following a long meeting of the Government's emergency Cobra committee, the Foreign Secretary said co-operation with the French authorities and Eurotunnel had improved.
He said: "I'm pleased to say we have seen a much improved level of co-operation and collaboration with Eurotunnel over the past 48 hours, with trains being cancelled where appropriate and in some cases trains being reversed back into Coquelles where there is a danger of illegal migrants being on board."
Mr Hammond added: "Finally, we are working very closely with the French authorities on putting together a joint plan to support returns to country of origin by illegal migrants seeking to enter the UK and those who are in the Calais area.
"France and Britain are determined to work together to lead the campaign in Europe for a more robust approach by the European Union to ensuring we get the returns of migrants to their countries of origin."
A number of measures were unveiled after plans to send extra sniffer dogs and fencing to Calais were labelled a "sticking plaster".
Landlords who fail to remove illegal immigrants who do not have the right to live in the UK - or who do not carry out checks on their status before renting out properties - could face up to five years in jail.
The measures will be included in the upcoming Immigration Bill, with the aim of making it more difficult for migrants to live in the UK after their visas have expired or applications for asylum have been rejected.
A consultation will be held on changing rules to remove taxpayer support for more than 10,000 failed asylum seekers living in Britain with their families.
However, both policies were already being worked on before the situation at Calais worsened.