Heathrow Express Train Wi-Fi
All Heathrow Express trains have been Wi-Fi-enabled to provide passengers with broadband speeds of up to 2Mbps for the 15 to 20 minute journey linking Paddington Station with the airport.
In order to use the service, you need to purchase T-Moblie HotSpot access. The T-Mobile card can then be used on the Heathrow Express or at more than 400 T-Mobile HotSpot locations within London.
So now you know, you can stay connected on the train, and yes, it even works in the tunnel.