With that kind of budget you are going to have to travel a lot, if you want to live in a nice area.
What do you mean in Camden? Camden borough or Camden Town? Although Camden Town is less than nice for a stroll, it is quite an expensive place to live. Most of Camden borough is very expensive, Hampstead, Primrose Hill, Swiss Cottage, and Regent's Park are amongst the most expensive in London (close to 1500 pounds per square foot to buy on a long lease). West Hampstead, Camden Town and Holborn are about average price for central London, the only places in Camden (borough) which are cheap are Kentish Town and Kilburn, and these straddle the border of the borough anyway.
At around 230 pounds per week, you may see some places in 'nice' areas, (like Mayfair, Hampstead, Belgravia, St. John's Wood, Marylebone, or Knightsbridge) but it is very likley that they will be in a bad state and very small, more likley a studio than a proper 1 bed.
I suggest looking at places further out.
Ealing has reasonable prices, and the express overland trains take just 7 mins. to Paddington Station. The tube takes about 40 mins. to Bank, less to the West end. It is quite green, but at the same time quite dense, has a good selection of shops, restaurants etc.
Chiswick is nice, and has stations on the District and Piccadilly lines, I don't go that often, but I think it's about 20 mins. to Knightsbridge, and 35 to King's Cross. It has a pretty well heeled population, and is genrally nice, if I could not afford Central, I would probbably choose here.
Clapham is nice also, a bit more urban than Chiswick and Ealing, but quite frankly a pain to get to if you are using public transport. It also has the stigma of being in South London (shootings etc.), Putney falls into the same bracket.
Further out, Richmond is very nice, as is Kingston. Richmond has express trains into the centre, which take a matter of mins. but I'm not sure about Kingston.
If you're lucky you might find a place in somwhere like Holland Park, St. John's Wood, Little Venice, or Chelsea. If you do, two bits of advice, check it out thoroughly, and go for it quickly.
Places I would stay away from include:
Fulham, ridiculous prices, far away, and full of people who want to live in Chelsea but cannot afford it.
Angel, hard to get to the Westend, and West London, is seen to be fashionable, but I just see it as dodgey. East London suffers the same plight.
Docklands, it is nice, but you are surrounded by dodgey areas, and although it is livley in the week, it is dead on the weekends. Surprisingly, given how physically far it is, it is very easy to get to the Westend and the City.
Southbank, unless being shot is an aim of yours.