I am interested in knowing if anyone has found some really cheap B&Bs or budget hotels in central London. I only want something basic seen as how we want to enjoy the city, not so much the hotel!

We'll be staying at Arran House. St. Margaret's is nearby in Russell Square area. People seem to like both of them. You might want to mention specific price range.

What's your budget?

I stayed in the women's residence at Imperial College once, during college holidays in the UK (not the same as American holidays). It was cheap, comfortable, clean, very centrally located in a posh neighbourhood (South Kensington) and felt very safe. However, it's only available to women. There might be other residences (e.g. those in Bloomsbury) that are co-ed.

Unless we know your target budget it is hard to siggest even "budget" places.

And Priceline is a good option in London - one can get 4 star hotels for less than the cost of a 1 or 2 star B&B. And if you bid down to the 3 star level you'd pay less than most any B&B that isn't a flophouse

I agree with Priceline.

If you want university residences, check here:
http://www.venuemasters.co.uk/holiday_travelstay.asp