Eurostar, the train operator, will start testing Wi-Fi access on its cross-channel services this year: But service won't be available while in the tunnel under the English Channel.
Another train operator, GNER, has been experimenting with Wi-Fi on its trains. It achieves coverage in tunnels by stringing together cell phone antennas to maintain the connection, which otherwise is backhauled via satellite. Apparently train operators are hoping that Wi-Fi services will draw customers back away from short-haul airlines.