Cant see you getting much change out of £50 pp per night. Some friends came to stay in B&B in Bloomsbury recently, and their rate was about £55 pp per night, although you did get a croissant and coffee thrown in fer breakfast ;)
Here are a few random prices (for a single room, midweek);
St Athans B&B (near the British Museum): £46
City Hotel Carlton (Victoria): £64
Kings Hotel (Kings Cross): £30
Mowbray Court Hotel (Earls Court): £45
St George Hotel (Paddington): £45
All from
http://www.hostelworld.com
(Don't be put off by the word 'hostel' in that URL. Simply carry out an initial search and then use the panel on the left hand side to deselect 'hostels', while adding in 'hotels' and 'guesthouses').