The pink thing is a limiting factor. If you're serious, check out this site for advice, http://www.kenrockwell.com/tech/recommended-cameras.htm
Despite being American, he's independent and the site is full of very useful photography tips and recommendations for a range of budgets. As a rule, Canon have the edge on compacts and they even make a pink one. Some of the model numbers are different in the UK but I think most that he quotes are sold here.
Agreed with smudge. I bought a Panasonic Lumix ZX5. Its pretty compact, but there are smaller models.
Leica optics (as used by Erwin Rommel) and a massive zoom... Good battery life and solid. Really worth it. http://www.panasonic.net/avc/lumix/
I recently bought the Panasonic Lumix DMC-ZX1 which does everything I want from a camera.
It is compact enough to slip into a jeans pocket, yet is large enough to enable a knuckle dragger like me to operate the nobs and buttons easily, it has a wide angle lens, x8 zoom, 12 mega pixies, and all the usual trickery you'd expect from a digicam these days, such as red-eye correction, image stabilisation, face recognition etc. It also gets a lot of good reviews for its picture quality. http://www.cameras.co.uk/reviews/panasonic-dmc-zx1.cfm
For a longer zoom (x12) there's the Panasonic TZ7.
Canon do a smart compact that's had a lot of good reviews (Ixus 200), but which is a bit too small and fiddly for my sausage fingers. I do think though, that Canon are a wee bit expensive in comparison to their competitors when put up against similar or superior spec cameras. http://www.cameras.co.uk/reviews/canon-ixus-200-is.cfm
I'd suggest a Kodak 'Brownie'. Very simple controls.
Seriously tho' any of the Canon iXus range, I've owned one for a couple of years now. In September, I bought the wife a new Nikon Coolpix S620 - at her request - it is absolutely superb. Highly recommended.
Mobile phones are never going to compete with a dedicated camera, it's all to do with size, despite what Phone makers tell you, your never going to get close to a camera quality with a camera phone with a pish poor lens and a tiny sensor, of course they may well come close to a cheapo Korean camera.
Ken Rockwell, interesting bloke, depending on your view point he's talks sense or he talks bolloxs, most photographers probably lean toward the latter
As most seem to agree, Canon takes some beating in the compact range, and there's me a Sony owner
Replaced my old Hp with a Canon Ixus 95IS a couple of months ago and can't fault it so far.
Normal photo quality is great, even very low light (for those xmas tree shots) is acceptable, and it's got easy enough controls along with a few more advanced features that don't get in the way when you don't want them.
It's only a 3x optical zoom but there are plenty of pixels available for digital zoom without losing detail unless you want silly size prints. Battery life (Li-Ion rechargeable) is excellent and it actually feels like it's properly made. It's also about the only one out there at the moment with a viewfinder, which can be surprisingly useful at times.
One thing to be aware of is it doesn't have any on-board memory so she'd need an SD card to go with it. 4Gb card holds about 1300 photos at maximum quality.
Cost about Â£170 when I got mine but seems to be around Â£125 now. Also available in pink.