If people Won't get off to allow a wheelchair user on, then people in wheelchairs won't ever be able to reliably use a London bus during peak hours. They are so busy that you just couldn't rely on one arriving with enough empty space during those hours. People in wheelchairs have to get to work and appointments in a timely manner and they will face this problem every time they try to catch a peak time bus.
Whereas the other passengers will be asked to get off the bus for a wheelchair user once in a blue moon. In the majority of cases they will be able to catch the next bus in 10 mins, or walk, and not be harmed by being a little late. In the rare occurrence that I absolutely had to get that particular bus I would just squeeze down the bus so I was out of the wheelchair space but didn't need to get off myself. I used to work shifts with a fixed start time but occasionally things do happen to make you late, eg if the bus was full, or late, in most cases people build a little leeway into their commute to allow for unexpected events, or their employer accepts occasional lateness.
Black cabs are expensive, you can't assume the wheelchair user can afford to take one to work every day! Individual car will get stuck in traffic congestion.
It's reasonable to stand in the unused wheelchair space as long as you make room or get off if the space is needed by a wheelchair user. London buses are often heaving and overcrowded at peak times so unrealistic to insist on the space being empty all the time, but people do need to vacate it promptly when it is needed.
I'm disappointed by the op's experience as I've mostly seen Londoners be helpful to wheelchair users on buses, vacating the space straight away. Also when I've occasionally travelled with a pram at rush hour (eg hospital appt), passengers have always squeezed along so I can fit the pram into the wheelchair space, it's really disappointing that nobody moved for an actual wheelchair.
London buses don't issue paper tickets, you pay by contactless so the driver wouldn't know who got on last, as some posters suggested. If you absolutely need to be on that bus and are standing, I'd suggest trying to stand in a different area of the bus so you aren't in the way if a person needs the wheelchair space.
What I think the driver should have done is turn off the engine and announce they will drive when the wheelchair user is able to board by approximately 10 people getting off. I've seen drivers do this before when people have refused to pay the fare or are behaving antisocially. It is very effective as suddenly all the passengers are putting pressure on people to comply! It sounds dramatic but I've never seen it take more than three minutes for people to then comply.
Generally I see people behaving really well on London rush hour transport, when I was pregnant people were very willing to make way for me or offer me seats, and even with a pram in rush hour (ill advised and I was fully expecting to have to wait a long time) people budged over to make space. I'm really sad that some people are so inflexible and selfish. I hope it was just an isolated occurrence and not indicative of wider prejudice against disabled people.