For the best budget accommodation, with a central location, I would recommend the St Giles Hotel. It is situated almost on the corner of Tottenham Court Road and Oxford Street, so you will not get closer than that. Rooms cost about £70 per night, or £35 each if double occupancy.
Rooms are small but perfectly adequate. Hotel has a bar and pizza-like restaurant - again adequate. But apart from the central location, another bonus is the health centre with its massive swimming pool and gym.
The address for the website is http://stgiles.com/
MOL on SRB's latest attack at BA: "It's like a little Chihuahua barking at a dying Labrador. Nobody cares."