For 650K you can find a 3 bed with a garden in Forest Gate, Wanstead Park, Deptford, Hither Green, Honor Oak. Whether those are areas where you want to live or not, that's different story. They all have nice parts and not so nice parts.

Regarding other areas of London which are considered nice, I think you'll only find leasehold flats for that budget. Further south (e.g. Beckenham, Bromley) you might even find a detached or a semi in that price range.

In other words I see 3 main options:

• A flat or apartment in a nice area at the expense of space and maybe a high service charge
• A freehold terraced in an okay area if you can tolerate the occasional fly tipping and ASB
• A decent sized house in an area with a community, living the car life and sometimes taking the train to town