I’m Caroline and this is my experience of getting around London with MS.
I have found travelling around London on public transport much easier since I started using a crutch. Prior to this I always felt a bit unsafe on my own, as I walk very slowly and wobble a lot. I felt people would push and not give me the space I needed, often making me walk more quickly than I feel comfortable with. The crutch makes everyone aware and I have found people give me room, don’t crowd or rush me and I feel much safer.
Escalators are a bit of a challenge - needing to stand on the right [in London] and hold on is difficult as I use my crutch in my right hand. Holding on is essential due to dizziness and I struggle to use my crutch in my left hand, so more practice is needed. When getting on and off tubes and buses people also seem to give me space and time to be safe.
I find on the London underground people will usually give up the accessible seats but not always. Other travellers on the tube do ask people to give up those seats (sometimes a bit aggressively), but it does make the point. Most amusingly, I got on a tube train and the carriage was fairly empty but someone was in the accessible seat, so I sat elsewhere, and a lady had a real moan at the person in the accessible seat for not moving. They moved and apologised to me and then I felt obliged to move to the accessible seat. However, people on buses are less helpful and tend not to give up their seats.