I play the clarinet, so I can speak with some experience, albeit not expert.
I was lucky enough to pick up a secondhand wooden clarinet at a very cheap price, which I still have and which sounds as good as any £1000 jobbie on the market.
I wouldn't suggest wood for a ten year old. With the best will in the world, they aren't always gentle with them and wooden ones are easier to break and harder to get good replacement parts for. If you spend between £200-£300 (new) on a good quality plastic/resin instrument now, it should take your child through to around grade 5, at which point you can then upgrade to a wooden instrument in the semi-pro bracket if the child wants.
Yamaha instruments are good. They are of good, consistent quality and sound, if a little sterile in character. They have a range of models from student to pro, and also have the advantage of holding their resale/trade-up value when the time comes. Parts are readily available, so if the child does manage to damage it, there won't be a lengthy wait to get it fixed.
You may also want to look at the Jupiter and Trevor James instruments, and there's a company in Yorkshire called Hanson, who make some very good instruments at very reasonable prices. Two people I know have bought saxophones from them and been very pleased with the quality.