And to add some more specific advice – I built a 24″ hardtail for him when he was 9 (based on a Kona Stuff 2-4 frame with a cut down Pace sus fork). If I was buying now (and new) I’d be looking at the Commencal Meta HT 24 or similar, but our requirements are disks and (in an ideal world) suspension.
If you can do without suspension then the Genesis Core 24 looks a really good option – plenty of room for some fat tyres for some cush.
Islabikes are great bikes – light and well kitted, but the Beinn 26 isn’t much of a mountain bike. Would be good if you want an all rounder, but it’ll get out of it’s depth fairly quickly on anything serious off-road. Ditto for Frog, nice bikes, a bit cheaper than Islabikes, a bit cheaper specced than Islabikes.
At 150cm he is definitely heading into 26″ wheeled territory though – which at least means access to decent sus forks. On a budget you’re best bet is building around a small hartail frame (eg 14″ Inbred etc, see that other thread for candidates) Budget will dictate new or second hand. There’s XS carbon hardtails to be hard on eBay for a few hundred quid. As said (Yak again) cranks are often tricky to spec – 150mm Thorn ones are good as 104BCD.
Oh and the bike he’s on at the minute is the Trek Fuel EX Jr. Review here/in the mag imminent when I can find the time to finish writing it!