I usually stay at the St. Giles hotel just off Tottenham Court road (1/2 block from the tube (Tottenham Court road -) prices range from ?89 to 129 depending on the time and size of room. You could try booking it here using Kayak or any other site.
I usually take Paddington Express from Heathrow ( online fares ?20 single -?34 return) , to Paddington station, takes 15 minutes (the tube takes an hour from Heathrow) then take the tube or cab (?11 to St Giles) if you are staying for more than 3 days in London buy the 7 days tube/bus pass for ?30.40 (zone 1 and 2) or ?60 (zone 1 to 6 - Heathrow) it’s worth.
You could try VRBO or Airbnb
St Giles Hotel, Central London, Bedford Avenue, London WC1B 3GH, UK, Tel.: +(44)0 20 7300 3000, Fax: +(44)0 20 7300 3001
http://www.stgiles.com/