Ok, a bitmore about the SENs.
I've never been called to the school to collect / comfort, he functions very well in a mainstream environment, average or just above average academically, loves school, very well behaved, no real sensory issues, has never had a meltdown at school. Problems that show at school are mostly not relating to other kids or knowing how to make friends / have conversations about other people's interests, plus finding story writing and comprehension difficult and some issues concentrating
This is an exact description of my DS when he was in Year 2. The "problem" issues you describe are EXACTLY the sort of things that got to be more and more of an issue as he got older. Other kids start growing up, playing less, chatting more, interacting in a more adult manner, having group conversations much as adults do. DS gives the impression hus conversation skills are fine when he's one to one with an adult, or a sibling. Put him in a group with boys his age and he is totally unable to keep up with the speed of the conversation, the dynamics of taking turns to speak, how one subject leads to another, he doesn't get the social niceties of showing an interest in something he's not interested in himself. His primary school friends were kind and tolerated him, but he was gradually getting isolated from his peer group. Living close to school meant he still had opportunities to socialise, going to Cubs etc with schoolmates, their parents and I have always done ad-hoc childcare for one another too, also we bump into them at the park etc.
As for the writing, comprehension etc, that all got worse too. As they get older the instructions and texts they are given by the teacher is in longer and longer chunks, maths problems writren out as words etc, all harder and harder to follow, frustration grows. My DS started struggling in Year 3, the school (state) did put significant support in place for him, with me leaning on them but it wasn't enough and DS, who is of above average intelligence would have been heading for the bottom sets at secondary school and social isolation. This is why I applied for and got his statement (it wasn't easy but that's another story).
The point of all this is that I thank my lucky stars he was at the local state primary not a private school miles away. I was able to be closely involved in his school and social life, was able to play an active role in ensuring he got the help he needed as he went through. The big problem for private schools and SEN provision is the cost, the support a child like my DS needs is significant and in the state sector there is a statutory process to obtain this support and its funding (although you might have to fight for it). In the private sector the money has to come from somewhere too and the options are to make parents pay for it on top of fees, to not take a child requiring this level of support in the first place or to manage them out once academic or behavioural issues start to manifest themselves. I am not expert on private schools but have a close circle of friends with DCs the same age as mine in private schools who are all in agreement with me that their schools would not provide anything like the support we have had from our state primary, also the academic and social skill abilities of the peer groups are higher so the gap is wider.
I would implore you to consider state schools. I take on board the Yr 7/8 gap problem, but there are ways round that when the time comes and public school may not prove best for him anyway. I would also look seriously for independent special schools. I'm not in your area and my DS's school doesn't start till older but there are others out there.