Anorak,
Just checking that you were in the plane as a passenger and not as a member of the flight crew!
Once in UK airspace, there are two possible routes you could have taken depending on the position of the inbound North Atlantic Tracks:
1) Eastbound over Southern Wales, passing Bristol, Swindon and Newbury and then into Ockham in Surrey (near Woking) which is the southwest arrival point for Heathrow. Then heading east over South London before turning left and then left again and over Fulham, Putney, Richmond and Hounslow before landing.
2) Southeast from Scottish airspace, passing Manchester, Birmingham and Milton Keynes and then into Bovingdon (near enough to Watford)which is the northwest arrival point for Heathrow. Then heading southeast over North London before turning right and then right again and over Fulham, Putney, Richmond and Hounslow before landing.
Can't help you with the routes outside UK airspace.
AI