Bexleyheath has looked like that for the last twenty years so I don't think it's ever gonna change any time soon and get gentrified. There are other areas nearby that already have been, a long time ago, I don't think BH will ever be on that list. It's had improvements of facilities in the last 30 years and quite a lot of building works but that's it.
I haven't been there for four years so idk how many empty shops it has these days, but when I lived nearby there weren't many empty. Which is usually a good sign.
You are never gonna get fancy shops there, Selfridges, fancy delis, that sort of thing. Locals don't have the money.
It's an alright area but as pp said it's absolutely heaving with kids after school. Actually, they tend to hang around for many hours after school. That said, I was going through there a lot between 3 and 5 and I never saw any kids causing trouble.
It has a pretty good ASDA, the best Lidl I have ever seen, a cinema and a bowling alley. It has a lot of buses that go to a lot of places.
Down the road you have Hall Place which is a lovely place to visit to feed ducks and geese. I believe they installed a small railway for children that folks were griping about ruining gardens. Idk how good or bad that is.
On the other side of the A2 a short bus ride away you have Bexley Village which is good for fancy restaurants, delis and some nice pubs.
Going back towards London you have Welling a short bus ride away which has a lot of shops and a massive Tesco. That's a bit more downtrodden and a bit more rough.
It's virtually on the A2 so if you drive, you have access to some pretty lovely areas of Kent to visit easily. Lots of crashes on a regular basis a bit further towards London near Blackfen often see it jammed up though.
There are definitely worse places to live near London on a budget. I imagine it's pretty easy to sell homes there due to the sheer volume of people needing to live there for work, and those wanting to access London.
If that flat is overpriced (I have no idea what the area prices are like) what about the ones opposite Lidl? They were 80% built when I was last there, so must be done by now.