My granddaughter is just turned seven. She has had a cheap pocket digital camera for a couple of years ever since her dad was given it as a freebie at a conference. She now understands the very basic rudiments of taking snapshots (hold the camera as steady as poss, don't shoot straight into the sun, try not to chop off people's heads, etc).
Recently when they came to stay with us I lent her my Panasonic Lumix FZ and told her she could take as many photos as she wanted and we'd go through them on the computer later. She managed to capture some excellent shots which she was very pleased with. We actually printed a few of them out for her Summer holiday scrapbook.
You probably know that the Lumix isn't a DSLR with interchangeable lenses but is what is termed a "bridge" camera. The advantages of this type of camera are that it gives very encouraging results in "Point and Shoot" mode and is also light and compact enough to carry around, snapping as you go. Also, it looks like a "proper camera"!
I haven't checked but I would guess that you could pick up a second hand camera of this sort for around £100