Hi Carolsherman-
DH and I stayed at the Holiday Inn Express Southwark the night before we left from Waterloo, paid £59 for the night plus breakfast (double with a sofabed). The bed was a bit squishy and hotel location is not exactly 'central', but for an affordable short stay before Eurostar, can't beat it (five minute taxi ride to Waterloo and 5-10 min walk to the river and Southwark tube). I wouldn't do a long stay there though or you'll throw your back out!
I'd also recommend the Premier Travel Inn chain, they're always affordably priced and the rooms look decent. They're all over the city but there's one in the County Hall building just next to the London Eye, so ideal location. Haven't stayed with the chain but it seems basic and affordable and would consider it. Also try searching tripadvisor, the reviews I've found on every hotel we've used are really reliable.
Enjoy your trip!
(Should clarify these are all London references!)