Eurostar officials canceled all scheduled services until Saturday at noon and warned that service for the rest of the busy holiday weekend would be "severely disrupted" due to extreme weather conditions.
"We strongly recommend that travelers whose journey is not essential change their tickets for travel on a later date or have their tickets refunded," the company said in a statement posted on its Web site.
Eurostar spokesman Bram Smets said service would be "very limited" on Saturday and Sunday because of the freezing conditions but said schedules would be normal by Monday.
He blamed heavy snow in northern France for the problems. Eurostar officials said the trains broke down because of the temperature difference between the cold air outside the tunnel and the warm air inside.
The company provides train service linking London to Paris and Brussels.
Eurostar officials said all the passengers who had been on the trains that broke down inside the Channel Tunnel were safe and had been removed from the tunnel.
The company said two of the disabled trains had been pushed by diesel trains toward a station in England and that passengers from the other trains had been transferred onto shuttles that brought them to train stations.