I am looking at purchasing advance tickets from Paddington to Bath. It looks like there is a significant discount if purchased in advance but the tickets are for a specific time. Flying into Heathrow that morning - anyone have any advice for how long it takes to go through customs etc assuming no problems? We would take the Heathrow Express from the airport to Paddington but that looks like we can just hop on any train when we are ready to go. Thanks for any help!! I know it's a bit of a gamble trying to time this!!