I have read this thread again some amusement.
Get a husband.
Move to Milton Keynes.
We don't have racism here.
Anyway, other people's opinions aside, I have a few things to add:
I think flat prices in London will continue to fall, and by the time you have your deposit together in 3-4 years, you might be looking at a far better, bigger quality of property.
I think around Croydon is a good idea, it's pretty diverse, has been for the decades I have known it.
I admire your determination to remain child free and single, however, I would also add, when you get into your mid 30s, it can get a bit tiresome. Friends couple up and reproduce, and if you don't keep making new (younger) friends, a lot of your social circle will be a lot less available.
London itself can grind you down over time. I was ready to get out by mid 30s, but then I only ever really worked and lived there because I never really felt I had any other choice. I never had the confidence to up sticks and remove myself to a completely different location where I knew noone. I didn't have the means, I didn't have the balls.
Perhaps in the future, when your career has developed to the stage where YOU can dictate the location of the work you take on, somewhere like Brighton might suit you better - say in ten years, for a longer term home. Always people coming and going, always something happening, not necessarily centred around family life, people of all ages in all the places.
I find your determination and reserve admirable, OP.
It's really interesting to see an increasing number of young people on this board in the last few months who are absolutely determined to not be financially screwed over with ball and chain mortgages, taking on ropey houses that haven't been maintained, and so forth. To an extent, it works in your favour that you are not going to have cheap credit thrown at you, because you can now observe from afar the spectacular fall out that's going to occur over the next few years from people who mortgaged themselves to the hilt (sometimes because they had no choice, sometimes because of wanting to keep up with the Jones). People who have never owned a home (myself included) are learning a lot of lessons from other people's past financial decisions (and an awful lot about governments and the housing market).
You keep doing exactly what you are doing because when you do finally buy, I have no doubt the end result will be absolutely brilliant.
(there are still some HORRIFICALLY racist areas in Kent, if the time comes and you want to head that way, do lots of research)