7dayshop does a stupidbright light of the type Kim describes for just over £30, but the battery's lower capacity than many, so run time may not be good.
http://www.candb-seen.co.uk/category-cycling.html does one for £37 or so with a higher capacity battery, & they also sell fresnel lenses & spare (& higher capacity) batteries & other spares & accessories. Their batteries seem to be as advertised, & they're very good on returns of faulty stuff, IME.
Trade-offs - Mrs B has a dirt cheap(£20 or so) Shenzhen Special retina-burner which has worked perfectly for about 5 years, but the original battery didn't last very long (a couple of years?), & of the people I know who've bought similarly cheap lights, some are absolutely fine, but others are very poorly made, some have dodgy connectors, & as Kim says, dodgy short-lived batteries are quite common. At the price, it's hard to say the lights aren't value for money, though.
AFAIK none have had a problem in rain. They're usually ordinary DC plugs, which work well in the wet. USB connectors aren't really designed for waterproofing, but I think some of the lights & batteries now have cased USB connectors for weatherproofing.
I think the cutoff between garbage, & basic but functional, used to be around £20 or a bit less. I'm not sure now.