You going over there to study or work? There are sizeable
Singaporean student communities in London, especially in LSE,
Imperial College and UCL. You might want to link up with their
Singapore Societies.
A place near Oxford Street is not going to be cheap, unless you are
talking about university hostels, in which case LSE has a few which
are around the location, except they are only available mostly to
first year students. It also depends on how close you want.
Actually central London is a rather pedestrian friendly place. A 20
mins walk is very common and rather refreshing.