What do these 8.5 million super-rich londoners do, if doctors can't afford to rub shoulders with them!?
So that's a weird mix where the rich lives with the poor, but the middle class is excluded. ( well, from time to time, one of the estate flat goes on sale for between 300 and 400K which is somewhat accessible to middle class, but then less than 20% of the housing on an estate are privately owned via right to buy scheme, and most of the time the original owner are still living in as they can't really buy better anywhere else )
edit: note that for nurse, there are help scheme available via key worker shared ownership ( you buy a share and rest the rest ). So you have more chance to find a nurse living in the center than a doctor.
Also note that the problem comes from the price explosion of private housing over the last decade. 10 years ago, where I was looking, there were estate, shared ownership (50% of 200K) and private properties starting 200K and up. Now, you have estate, share ownership (25%!! of 600K) and private for 600K and up. The salaries are about the same and the level of help to access government assistance hasn't changed much either. So you can progress from poor to lower middle class, but then there is huge gap to be able to afford your place.
In my area, the cheapest you can find still in inner London, the average price of a 2 bed is 300K and new flats are 500K and up. All but 1 landlord in my building bought their flat since 2007, all the rest bought them between 60K and 80K when they were built in 2000.
That's the tricky bit when thinking about fixing the problem. Even though only people that can afford 300K and more can move in, the majority of private landlords are of modest means and that's going to be that way for decades.