Apparently the rule is that if you attempt to enter the UK without the correct documentation then you have to be processed at your point of entry, ours being Terminal 1, so the Border Force at T5 wouldn't do anything until we went by bus back to T1 to have an interview and for them to run background checks.
It was BA who sorted out the rebooking and Sofitel, as they stated it was a known LHR problem and we hadn't done anything wrong by following 'Flight Connections'.... They were very embarrassed! We only got to the Sofitel after returning to T1 and getting through the checks, then we had to head back to T5 for around 5 hours sleep!
It's actually a simple problem to fix, all they need is to produce some signs at T1 that say 'International Flight Connections' and train the agent to direct domestic pax out of the baggage claim, onto the Heathrow Express to T5... Would have done that had we realised!