You can look for flats online using the internet or through real estate brokers. There are a number of websites that offer listings of flats and apartments for rent in London. You can try www.intolondon.com or www.gumtree.com both of which have real estate listings. Most big real estate firms have their own websites as well.
In the area that you are interested you can get in touch with local real estate brokers. In most cases they charge a commission or fee equal to one or two months rent. Most newspapers also carry listings of rental property in their classified sections.
Depending on the area you are interested rents can vary greatly. Rents in the West End and central London will definitely be higher than what you may have to pay for something similar in Harrow, Kenton for instance.