People tend to check in during these times:
Heathrow Express is the best way to London!
No wifi on trains. not even in 1st class :(
PAD-->Bristol Temple Meads on a Sunday afternoon. The busiest train I have ever been on.
Platform numbers come up on the National Rail iPhone app way before the station departure boards.
Sometimes you can piggyback on the Heathrow Express wifi while your train is at the platform.
To save money to Heathrow use the Heathrow Connect