During a recent trip between London and Edinburgh, I found free WiFi on the entire National Express train.
This is truly unique – at least amongst UK trains.
Added to this, each seat in the train (standard class included) had a power socket. Kudos to National Express for such facilities. Though, I must add that, on my return trip, all power sockets in my coach were faulty, so I couldn’t use the free WiFi for more than two hours out of the total trip duration of nearly five hours, after which my notebook PC’s battery ran out.