Eurotunnel and Eurostar are going to have some explaining to do. The same problem occurred in 1995, 2002 and 2003. They appear to have been completely unprepared for it to happen again with totally inadequate contingency measures in place.
From the Guardian 1st Feb 2003:
"The winter weather that has ground nationwide transport to a halt has taken its toll on the Eurostar service. The extreme, icy conditions wreaked havoc for passengers on the rail route which connects London with mainland Europe.
Trains running in freezing temperatures lost power as they hit warm, humid air in the Channel Tunnel yesterday causing them to break down, a Eurostar spokesman said.
Condensation formed on the trains when the cold engines entered the tunnel where the air was much warmer - about 28C (82F) - hampering electrical systems, according to the official. "It knocks out the overhead electrical supply," he said. "
http://www.guardian.co.uk/uk/2003/feb/01/transport.world