In reply to Euan Todd:
I like, for the performance:size ratio, the Panasonic Lumix TZ series. You'll pick up a perfectly good 2nd hand TZ30 for about £60 or new maybe £130?
Mind you I'm pretty careless and therefore hard on stuff and have broken them so currently trying a change of tack in case they're more robust, and gone onto a Canon Ixus 230HS which I bought 2nd hand for £30. It's even smaller (tho with less zoom) and really good, and I'm now thinking of upgrading to the later IxusHS265 because it has a wider angle lens and 12 x zoom rather than the 8x I have on mine.
I probably should go with the tough type cameras recommended above but I think they're generally limited to around 3x or 5x zoom and I like a bit more flexibility in that regard.
By the way I'm not a camera buff, just a punter.