I'm not in the UK either, and where I am it is quite common for parents to do as you are thinking of doing. Not usually by the time they have got to 10, admittedly, but certainly having them start later.
If the "only" issue your child has is that he's not the brightest star when it comes to academic achievement then all this round of specialists that (if I understand correctly) the school have pushed you into pursuing, seems very heavy handed. It almost reads as though they want him shunting off out of their way.
In all honesty, if that is all, then I wouldn't. I really wouldn't. Here's why. In dd's class there were 2 kids who were a year older than their peers. And it showed, the older they got, the more, frankly, out of place these two seemed. So much older, so much more mature, a year at that age, can be a hell of a difference. I know you are looking at it from the other way round, but there were these 2 kids who had almost 2 years on the youngest in the class, and by the time they were going on 13, they were stuck with just turned 11 year olds. From full on puberty- voices breaking, moustaches...to tiny things playing with model cars still. And unless you are then going to get them to eventually skip a year- it persists.
On the other side, I teach EFL and have a class of 16 yr olds, some going on 17 some just turned 15....one of the 15 yr olds mother came in last week and went on about him being the youngest and still a baby
and how she regretted having sent him to school when he was so young. The teacher with me just guffawed at her and said "Mrs X, how much longer are we expected to accept the fact that a kid is older or younger than the rest of his class as an excuse? It really doesn't wash after about the age of 7."