lurker surfacing... I've lived in London all my life, and I have to say the truth is often just not like this. Areas get reputations which aren't always justified and can change quite quickly. In the context of house prices its often those people who look beyond the cliches and easy jokes who do very well.
30 years ago people were saying Islington and Notting Hill were overrun with gangs and you wouldn't survive the walk from the busstop. 20 years ago Battersea was supposedly a no-go slum. 10 years ago you couldn't go to Hoxton or Shoreditch without an SAS guard. And all the time that these wise sages, just as now, stayed renting in the 'burbs, waiting for the right time and place to move, others looked at the beautiful housing stock, the easy transport (bus or cab, not tube) to work or play, and acted. Now its the time for Walworth/Camberwell and places like Bethnal Green (far "edgier" than SE5). If you can't make your own mind up, you could do a lot worse than follow "the pink pound" and the "arty" which is piling into these areas. Just as they did when they were priced out of Belgravia and went Chelsea. And then Parsons Green. No one gets prizes for being wise after the event.
As for Addington Square, I know it, have friends there, and would LOVE to live there. Far from being the "wrong" side of Camberwell, its on the "town" side, a good mile closer to work and play than Camberwell Grove meaning a quick bus over any bridge. As for Burgess Park its in the middle of a £6 million re-fit, with improved modern lighting landscaping etc. Expensive? compared to what? its a listed, no-thru-road, Georgian and Regency square on the edge of zone 1. A quarter of the price of Highbury Fields or Niotting Hill and half the distance to Trafalgar Square. Honestly, if I had the money...