While Ebuyer are flogging the
Samsung S630 for £44.99,
Argos have a selection of cheap digicams, and they are very good about returned items.
I think the really cheap branded (Kodaks, Samsungs etc.) digicams do tend to use 2xAAs (thus you aren't paying for a Li-ion battery), but the performance and size savings you get from Li-ion cannot be ignored.
Always check out the user reviews on DPReview:
Digital Camera Database: Digital Photography Review
You can learn about many of the fiddly things a reviewer might not think to mention.