Eurostar's passenger bill for the collapse of its services before Christmas is likely to top £10 million.

Around 2,000 passengers were stranded in the Channel Tunnel when four trains broke down. They were trapped in nightmare conditions for up to 18 hours. A fifth train also broke down and had to be towed back to Ebbsfleet International.

The failures were caused by the extreme cold weather and snow affecting the trains' electrical systems. More than 100,000 passengers hoping to get away for Christmas were affected by the numerous cancellations that followed, including many from Kent who hoped to travel from Ebbsfleet and Ashford International.

The disruption, made a lot worse by poor communications, severely damaged Eurostar's reputation and prompted the setting up of a high-level probe led by Christopher Garnett, formerly from Kent and ex-boss of GNER railways.

Eurostar bosses are trying to repair the damage with a combination of compensation, apologies and promises of better future performance. Most passengers are receiving travel vouchers, with the worst affected also handed £150 payouts.

In a letter to customers, Richard Brown, chief executive, said: "I am acutely aware that we have to win back the trust of our customers following the disruption to our services before Christmas. We failed to deliver the standard of service you expect and I apologise unreservedly for the problems that occurred."

He said Eurostar was doing all it could to "minimise the chances of further disruption. The extremely adverse weather conditions of the last few weeks mean that some delays and alterations have been inevitable, but following a series of tests our engineers have completed a number of modifications to ensure greater resilience to extreme winter weather."

Mr Brown conceded a need for better information and to ensure that the service was more robust and reliable in bad weather. He said Eurostar had implemented changes to achieve these aims.

He admitted to The Sunday Telegraph that the disruption had been a "disaster" for Eurostar and the company would accept all the Garnett recommendations.

"I take responsibility for what happened to our passengers, and our operational contingencies, frankly, weren't up to it," he said. "We recognise we've got a way to go to recover the confidence and trust of our customers.

"A lot of things went wrong. Hands up, a lot of mistakes were made. The purpose of the letter is to say the review is under way and we want to reassure our passengers. We recognise we let a large number of passengers down very badly on December 18 and also in the subsequent disruption."

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