LHR TO BUCK PALACE AREA

Look at Heathrow Express which goes to Paddington Station and see if that would help you. You can Google it for lots of information. There is a somewhat slower train on the same route that is a bit cheaper. I can't remember the exact name of that one -- Heathrow something.

TfL produce a special map which details stations where you can avoid stairs (ie escalators / lifts or a combination of both) from platform to street, or to change. http://www.tfl.gov.uk/assets/downloads/avoiding-stairs-guide.pdf This is a great map and it should be more widely available at stations IMO. Depending on exactly where you are going, Green Park, Hyde Park Corner or Sloane Square may work for you (the latter is step free only on exit). All stations at Heathrow are step free.

Just the info I needed; thank you both.

If traveling by Tube, the Westminster stop is supposed to be wheelchair accessible. I think you could take the Piccadilly Tube line from LHR, transfer without steps to the District line at Hammersmith, then exit at Westminster. From there, you are still a distance from Buck House, but may find there are no steps. I don't know if all corners have wheelchair ramps. If you are heading for your hotel, you might consider just taking a cab, either from Paddington Station or from a Tube stop. I've started doing that, and find it makes travel so much easier. I do this only when I'm traveling with luggage. It's easy to find cabs at train stations. Tube maps show all the wheelchair accessible exits. If you can get a map and study it, you can create your own itinerary. It still isn't easy. In the Tube, entrances and exits usually have a separate wide place for pushing luggage thru. It will be at the end of a row of turnstiles. Lacking a special exit for luggage, push your rolling luggage ahead of you in order not to get it caught in the gates.