Eurostar will be running a limited service on Sunday, but the company is appealing to passengers not to travel unless they must.

All services were cancelled on Saturday, following the breakdown of several trains in the Channel Tunnel. Eurostar CEO Richard Brown has apologised to all those who were affected, and the company will pay compensation of £150 to all the passengers who were on eight delayed trains as well as a full refund and a free return ticket.

Both the operator and Eurotunnel have been facing severe criticism for the way passengers stranded on up to five trains were dealt with. An estimated 2000 passengers spent up to six hours in the Tunnel after their trains had become stalled inside.

It's thought the faults were triggered by the change of temperature when the trains passed from freezing conditions in northern France to the warm interior of the Tunnel, which is said to be typically 25 degrees C.

One passenger told the BBC that after several hours those on board his train organised their own evacuation, and made their way via the central service tunnel to a Eurotunnel shuttle which took them back to Calais.

Power on board at least some of the trains failed completely, leaving the passengers in darkness.

Disruption has also been occurring in northern France, where many trains have been delayed by the bad weather. Both TGV and Thalys services have been among those affected, and problems were reported as far south as Paris, where some RER services were cancelled.

More snow is forecast for northern and central France, Belgium, the Dutch coast and eastern Britain.