For around £350 she could get a Sony Nex 5N + kit lens which has great image quality (just as good as any entry level dslr with kit lens - same sensor size) in a reasonably small package. She may find the 18-55 zoom too limited though? You could add the 55-210 zoom
but that's another £200 so way over budget and it's quite big relative to the camera size (but good quality and nice to use).
Otherwise an Olympus Pen as suggested - the Olympus E-PM1 + 14-42mm & 40-150mm lenses is £300 @Jessops which is not bad as the 40-150 lens on it's own costs £180. If she doesn't want to change lenses, Jessops also have the same camera (Olympus E-PM1) + 14-150mm lens for £450 (which is okay as superzooms go and an ideal all in one solution for travel) - again an excellent price as the lens bought on it's own costs £430!
The Sony Nex has better image quality than the E-PM1 (especially in low light) but the Olympus has smaller, lighter lenses.
Both have the art filters/effects mentioned including selective colour.
Neither are the latest models (hence the lower prices) but with the exception of the Nex F3, all the latest model equivalents are over £400 - the cheapest is the E-PM2 @ £500 with 14-42 lens. The price should drop over the next several months if she is not in a hurry. The benefits of the new model would be a better sensor (almost as good as the one in the Nex 5n) and a touch screen. (The Nex 5n also has a touch screen). The Nex F3 is £320 after Sony cashback:
http://www.amazon.co.uk/gp/product/...B14&linkCode=shr&tag=1567&psc=1&s=electronics but again this is just with an 18-55 kit lens which may not give enough reach as wanted. It has the same 16mp APS-C sensor as the Nex 5n and the other current mid-range Nex models (5R and 6) and also has a touch screen.
For an all in one solution (if you can stretch to £50 over your £400 budget) I would go for the E-PM1 and 14-150mm lens - this gives a very good zoom range from wide angle to telephoto due to the X2 crop factor of m43 cameras and is very light and portable, so ideal for travel. Image quality while not as good as the Nex or a dslr is good enough for most people as you can see by the sample photos here using the 14-150mm and various micro four thirds cameras including the E-PM1:
http://www.mu-43.com/f80/olympus-14-150mm-f-4-5-6-image-thread-3794/
One downside is the lack of a viewfinder (in bright sunshine for example) and so needing to use the rear lcd screen for composition and framing, but coming from a compact she may be okay with that? Both the Nex and the Pens can have an optional external viewfinder added but the cost is quite high at an additional £100 to £200!
You may have to purchase fairly soon if you go for the Nex 5N or E-PM1 as they are discontinued.
Reviews:
Nex 5N
http://www.ephotozine.com/article/sony-nex-5n-aps-c-mirrorless-review-17686
Nex F3:
http://www.ephotozine.com/article/sony-nex-5n-aps-c-mirrorless-review-17686
Olympus E-PM1:
http://www.ephotozine.com/article/sony-nex-f3-mirrorless-camera-review-19837
Olympus 14-150 zoom lens:
http://www.photozone.de/olympus--four-thirds-lens-tests/645-oly_m14150_456
