The high volume of traffic is causing delays of up to one hour to passenger Eurotunnel services at Folkestone.
Hundreds of Eurostar passengers were stuck on trains for hours overnight after an overhead cable problem.
The problem, at Lille in northern France, affected nearly 700 passengers travelling on yesterday's 6.01pm London to ParisEurostar service as well as around 600 who were on the 6.04pm London to Brussels train.
After not moving for many hours, the passengers were only able to complete their journey when diesel trains arrived to tow the stricken trains to their destinations.
A Eurostar spokesman said the Paris train had finally arrived six hours late, while the Brussels train had got in nine hours late.
The spokesman went on: "There was a failure of the overhead power line just outside Lille.
"The passengers on the Brussels train are entitled to twice the amount of a complete refund plus a free return trip, while those on the Paris train can claim an entire refund plus a free return trip."
Work is continuing to get the Channel Tunnel up and fully functioning.
An evacuation took place yesterday with hundreds of passengers left stranded when a train broke down and a shuttle became stuck.
Delays and cancellations are likely to continue today.
Freight services are taking up to two and a half hours as only one line is working.
Passengers services are running normally at the moment.
Video. Hundreds of passengers were trapped on a broken-down train in the Channel Tunnel today. The French-bound Eurotunnel passengers shuttle train came to a halt about a quarter of the way through the tunnel after a problem with the overhead power line.
The incident has led to some other services being cancelled and long delays for travellers.
Malcolm Shaw reports.
Hundreds of passengers have had to be evacuated from a broken-down train in the Channel Tunnel in an incident which has led to long delays to travellers. Brian Waite, who was on the Eurotunnel train, is in the terminal building in Calais and has been waiting for almost six hours.