London Short stay- September 12th to 18th,2009

Hi all ILs in London! This is Uma from Chennai. I hope some of you can help me. My daughter (30yo) and I (55yo) are visiting London from 12th Sept to 18th. It's a dream-come-true for us as we had planned such a holiday years back and somehow it didnt materialize then. And now all of a sudden things are happening and we are so excited. I really need your advice since I told my daughter that I would take care of our accommodation. The more I look at ads, the more I am confused and the exchange rate isnt making me feel too good either! What I need is:
1. Accommodation for 2... self catering shortlets (ensuite) would be best
2. Safe, clean, bright place
3. Very close to tube/ bus station
4. Not too far from the centre
5. The budget has to be really small
I want to take advantage of your experience to get myself a place. Please dont forward any websites to me...i am going mad just looking at websites! If you know of anyone who is willing to put us up for this period at reasonable cost, please let me know. Thanks in advance! Have a good day!