There is lot of one bedroom flat available for sale at rental in London. For that, either you can search online or directly contact some good property consultant, which can assist you to find flat, as per your choice of location and budget. I am not a landlord but I can suggest you one property consultant group i.e. http://tinyurl.com/olery6f that has large property database in every area of London. Hope you find your dream flat at reasonable cost.