According to Eurotunnel, which owns the rail route between Britain and France, none of its car-carrying trains are able to operate.
Later, Eurostar wrote on its Twitter page that traffic had resumed and services were slowly getting back to normal.
Clients informed being stuck on stationary trains for about 80 minutes.
Power outages problems emerged after noon on Thursday and were fixed at 1.30.
Eurostar is a high-speed railway service. Its trains run through Channel Tunnel connecting London with a number of French and Belgian cities, such as Avignon, Brussels, Lille, Lyon, Marseille and Paris.
Eurotunnel Le Shuttle is a company that allows people to carry their vehicles through the Channel Tunnel by rail.