Coming back to this response from OP to my earlier post, because maybe I'd better clarify:
It seems to me that we think in two different ways when we think ‘gentrification’. One class of people take it to be a massive price hike that could be used to get to a better area, even if it means a bit more commuting. The other class of people take it to be related to the population of that area.
NOt London, large city in the North of England. By borderline - three "respectable" working class districts, quite a lot of social housing, but they had an okay feel to them. Two didn't exactly gentrify (maybe that is a London-centric term) but they certainly became safer, less crime, less vandalism, schools improved. The area I bought in went downhill in the sense of kids stealing cars, setting them on fire and then pelting the fire brigade with bricks! I had four burglaries in eight years.
So I guess what I'm trying to say is if you're working from a limited pot of money (I am very much team "somewhere to live" rather than team "forever home", given my income), I have learned the hard way that yes, you do buy the more run-down, smaller house in the better area, every time. Because taking a gamble on a just-about-okay area can go really badly wrong.
Over the course of 30 years I've gone from 2 bed terrace, to 1 bed flat, then back to 2 bed terrace, where if I'd made wiser decisions (or had a crystal ball) I could maybe have spent the same 30 years going 1 bed flat, 2 bed terrace, 3 bed semi. (Having said that, the 2 bed terrace worked out for me in the sense that I was made redunant, but could keep the mortgage ticking over during the financially hard years while I re-trained, by taking a lodger - something I wouldn't have been able to do with a 1 bed flat).