Usually I would say to try your local independent wreck, but, tbh with little kiddies bikes, go to Halfords. The Apollo bikes are ok. And when they have a good offer on, very reasonably priced. It should last him until he's too big for it without too much going wrong. Get the largest wheel you can, probably a 20". 18" wheels are a no no, as they are not standard size (as the traditional jump from 16" to 20" seems a lot, and the manufacturers realised they could flog an extra bike). As he's confident, as long as he can get his toes on the ground, he should be fine.
Second hand or ebay will always be a pain, as you're looking at £30+ to get it checked out and fixed up. Kids tyres perish v quickly, and the cables sieze up inside, even though they look ok, thus the brakes generally are buggered.
I've shit loads of locks left over, I'll pop one in the post for him if you like!