Just as an afterthought for you T163R, some London terminus stations you can get around asking but don't have a problem.
London Euston, Kings Cross, London Paddington, London Victoria and London Waterloo you can get around if you get the right platform. If you go to:
Euston:- either far end but platform 2/3 is the best
Kings Cross:- platform 6/7, all of the other platforms are gated off
Paddington:- either platform 1 or platform 8? I think it's eight because they are not barried off
Victoria:- platform 2, insert your travelcard into and it will let you through no problem
Waterloo:- only been once and used platform 16/17 but it is hit and miss with them. Sometimes, they will come up and see what you are up to but sometimes, thy don't bother.
The termini that you might have a problem with is London St. Pancras and London Fenchurch Street. St. Pancras, the staff are very friendly there and they will let you through on either the domestic or international side. London Fenchurch Street is difficult to access because there is no direct tube station, nearest is Tower Hill/Aldgate but if you go to the reception desk on the left side before the barriers, they will more than happily issue you with a pass.
The only two you might have a problem with is Marylebone and Liverpool Street. Marylebone, you ask at the gates and they then call down the station manager and give you a decision to your face but normally, they are fine. Liverpool Street, try at your peril!
Hope that helps you when you come over