"Reasonable price" might mean different things to different people, and I don't really know what your threshold is. I also don't know what's available in the UK. But in the States, for a small steel-string guitar it's hard to beat the Baby Taylor. You can get them for around $250 American, which might be more than you're looking to spend. But it's a real, quality instrument that plays well and sounds good. I agree with one of the other commenters that you need to get an instrument aht is good enough that your ten-year-old won't get frustrated and give up. And the advantage of the Baby Taylor is that it will continue to give your child pleasure even after he/she graduates to a full-size instrument -- it's a great travel guitar, and adds a somewhat distinctive sound to ensemble playing. OR you can steal if back from your child after he or she moves on to something larger.