would appreciate any suggestions for reasonable accomodations for 2 for 1 month stay in or very close to london central....I will be relying on public transport.

If you are going at certain times of year, you might be able to use student accommodation. See here:
http://www.venuemasters.com/venues_az.asp

What do you consider reasonable?

traveling to london late july through late august 2005. I would like to be in the $100 US daily range....

Well - you are traveling at the right time of year to use college/university housing. The London School of Economics, King's Colleg, and the University of Westminster among others all have really reasonabel B&B and self-catering accomodations in very convenient locations all over central London.

Thy these sites:

www.lsevacations.co.uk
www.kcl.ac.uk/kcvb
www.wmin.ac.uk/comserv

sorry for all the typos . . . . .