I’d suggest East and Southeast London. East London is getting gentrified though and has become ‘hip’. BUT it also has lots of warehouses-turned-co-working/startup spaces. It’s also lots of fun and creative, with markets, amazing cafes and street food.
SE is very cheap, but with lots of problematic and ‘poor’ areas. It’s not very well connected either (no tube, but there is overground and railway). Because of lots of immigrants, it’s culturally diverse, with small shops and food places.
If you don’t want in those areas, try NW or N, but mostly zone 3 <, if you want a whole place to yourself. SW and W is posh.
Btw, £1000 for a whole place or in a shared space?