No.
DS was going through a really difficult point at primary and he and his mate were being bullied. We seriously looked into alternative options. We have friends with kids at private school who are doing amazingly well.
BUT they don't have many friends and much of a social life because they live so far from their class mates. That makes things tough.
And they aren't doing amazingly better than other friends kids who have gone to the local high school. So where's the benefit ultimately!
DS currently has a very close friend who he's exceeding close to. In the end we felt we'd ultimately do more harm to them both if we moved him. It's a friendship we feel is likely to be one of those that runs from nursery to the end of school. It's a rare thing and he's so lucky to have it. We feel that's something that you can't buy.
He has lots of opportunities outside school. We do our best to facilitate them. If he went private he'd actually lose out on a lot of these because of how much time he'd spend travelling to and from school. Yes he could do some things in private school but not all. It wouldn't be a step up, just a step sideways.
I am unconvinced that private school is the great networking opportunity many suggest either. Those who I know who went private really don't have those contacts. Several of them have very average jobs and are very mediocre as individuals. Over confident and arrogant with a lack of self awareness aren't things I particularly wish DS to aspire to.
The class sizes and the attention sound appealing but it also narrows the pool of people you can socialise with - both as acquaintances and as friends. There's a kid around the corner who was in my son's class. He was pulled out and sent private. Poor kid just hangs out with his older brother now and is reliant on mum taking him everywhere. He really could have done with socialising with kids from a range of backgrounds (various specific reasons) but instead his world has got narrower.
Meanwhile bullying over - DSs confidence is great. His friend is a massive part of that. They are so positive and supportive of each other. He's a bit of an oddfish but he feels he belongs all the same. I can't tell you how much I wish I'd had that at his age.
There's moments we wobble and think 'what if' but no I don't he'd benefit enough to make it worthwhile.