Depending on your budget then you may want to look at Acton, there's some pretty reasonable places there. If you've got a bit more money, then maybe West Hamstead area?
Do you absolutely have to live in London? If you work in Acton thats easilly commutable from places like high wycombe which will be half the price of most London places. Kensigntons a bit more of a trip but still not too bad.
All our friends are in London, and the cost of commuting from outside sometimes offsets the savings.
I think I just found the most incredible bargain, for a 2 bedroom place! Likely to be a mistype though, has to be!

Just the thought of 1k a month for a 1 bed flat/apartment sounds astronomical. Thats more than a lot of people earn a month before any taxes.

Lambeth!