Eurostar was criticised for its response to the travel problems at the time
Eurostar has admitted that it expects to pay up to £10m in compensation to passengers affected by the travel chaos before Christmas.
Thousands of people were stranded in the Channel Tunnel when five trains broke down in December because of condensation in their electrics.
Eurostar cancelled all services for three days to establish what went wrong and carry out safety tests.
In a letter of apology, Eurostar said improvements had been made.
Chief executive Richard Brown 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.
"Going forward, we need to demonstrate to you that we are doing everything possible to provide the most robust, reliable service during periods of severe weather.
"We are also very aware of the need for better information."
Mr Brown said the firm had strengthened its communication processes to provide better real-time information, increased the amount of food and drink kept on trains and developed a special timetable for extreme weather conditions.
He also said when the weather was bad engineers would check the trains before they entered the tunnel and there would be speed restrictions.
A review is being carried out into what happened. It was commissioned by Eurostar and will report by the end of January.
Mr Brown added: "We can't guarantee that Eurostar will never again be subject to extreme weather disruption, but we will do everything in our power to ensure that the chances of disruption are minimised.
"When disruption does occur we will provide our customers with the care that you rightly expect."