I own in Lee SE London, its nice round here. I’ve owned in the area for over 20 years.
Having said that if you are looking to hop on the housing market now my advice is DONT. Wait. House prices to earning multiples are still very high and houses remain overpriced in London. House prices have had a long run up for over 10 years and when markets turn after such a long period the falling market is not going to be over quickly. Nobody can tell how far it will fall or whether it will just level off but there is no way it can start going up again for a good couple of years or so. Banks arent lending and its going to take at least that long to rebuild their balance sheets so they able to lend.
I know it seems like you are chucking money away renting but you should sit tight and wait, you are in a good position to pick up a great bargain later or worst case for you is that prices will be flat and not gone up.