My boys are heavily into BMX. Tho I'm in the USA. Check out danscomp.com to get a feel for what brands to get. Mongoose these days has gone to junk. Sort of thing you find at Target or Walmart.
As a 10 yr old just go in and get him a 20.5 top tube... Which is basically adult size. You can go smaller as in 18.5 top tube, but he'll quickly outgrow it.
Two types you need to be aware of.. Race bmx which is all aluminum with big cranks and will quickly break at a freestyle park, but are absolutely fine for road use and freestyle, which are heavier, (chromoly rather than steel for the better ones) smaller cranks and a lot more durable.
Redline are a good known brand for Race, and freestyle well, there's loads, Haro, Sunday, Cult, the list goes on.
I have 6 bmx's in my garage 3 race and 3 freestyle.. All get used.