Hi Akatrin,
Have had a look on
Find properties to buy, homes to rent, overseas houses and new homes on rightmove.co.uk That's one website that does rentals as well as property sales.
Do you have any idea where you'll be working?
DO you have you any idea about how much you'll want to pay?
Do you want to rent a flat by yourself or share a house or flat? If you want to share then there's another website as well
Flatshare - House Share & Rooms to rent 190,000 Flatshare ads in the UK which is specifically for house & flat shares.
As Stravinsky suggests you may be better off travelling into London from the outside. I lived just North of London in Hertfordshire and I could travel into London on the Thameslink in about 25 minutes to Kings Cross. Of course you also need to take into account the travelling costs from anywhere outside London since that may not be that cheap either depending on where you are travelling from, although travel cards are available.
Hope that helps,
Karen