Many now have WiFi - according to Which
Wi-Fi hotspots
Wi-Fi on UK train services
Virgin Trains
Virgin Pendolino and Super Voyager trains have Wi-Fi access available with either a one-hour or 24-hour pass. Virgin Trains Wi-Fi is provided by T-Mobile so passes can be used at any of T-Mobile's 20,000 Wi-Fi hotspots. First-class passengers get free Wi-Fi on board.
National Express
East Coast Trains offers free Wi-Fi access on all its trains.
Eurostar
Eurostar offers Wi-Fi hotspots at its major UK stations, including London St. Pancras International, Ebbsfleet International and Ashford International, operated by Cityspace and The Cloud.
Business Premier customers get free Wi-Fi internet in Business Premier Lounges, and free Wi-Fi access is available to all Eurostar customers at St Pancras International.
Heathrow Express
Heathrow Express – on-train Wi-Fi access is available via T-Mobile HotSpots between London Paddington and Heathrow Airport.
Grand Central Trains
Grand Central Trains offer free Wi-Fi throughout their trains.