Thank you SO much to everyone for your responses - it's really appreciated 
You'll be pleased to hear that I did speak to the teacher @Motheranddaughtertotwo , she was lovely - said she had absolutely no idea that he wasn't always happy at lunch time, and told DS that he could always find her or a dinner lady in the playground if he needed help or company. He was reassured by that but things haven't been great since half term, the boy he thought was his best friend doesn't want DS to play football at all with him any more, and has started physically pushing him away 
I wasn't keen on this boy before TBH as he seemed to blow hot and cold and DS never knew where he stood, but they always got on fine - maybe it's because this boy (let's call him Alfie) is really keen on football and knows DS isn't (and yes @Puffalicious, his dad is mad keen as well and very pushy!). DS's birthday is in September, he's had two parties (2021 and 2022) both of which Alfie came to; Alfie's birthday is in December, he told DS that he 'forgot' to invite him to the 2021 party, and I found out over half term that Alfie had a birthday party last year as well which he didn't invite DS to I know that Alfie didn't have to invite DS, but it just seems so mean spirited not to invite him to a (quite large!) party when DS always invited Alfie.
@OhsoNat DS's teacher did say that the school were thinking of offering different sports at lunch time, I think it's just dependent on them having someone available to supervise, which they don't always! @Cashew22 he would prefer to play something like basketball or dodgeball if he has to be outside, but there's no option to do that, it's football or nothing...
@Victoria3010 I've tried DS at casual football clubs but he's just not interested! I offered for him to join the local club as that would give him a social circle but he was even less interested such a shame as I think that would help, but it's just not his thing, which is fine. @mollyfolk I asked DS again about the two other boys who don't like football, but he thinks (rightly or wrongly) that they're very much a pair and don't want him to join in.
@Findinganewme there are a couple of boys which DS has met through other interests who he'd like to hang out with, but either I haven't heard back from the parents, or it gets too tricky to coordinate it between schedules... then it turns into a chore and I feel bad that DS doesn't see other people, but from what you've said it may not always be worth the effort anyway!
DS would love to take his Pokemon cards every day @msmatcha but school only allow it once a fortnight! I guess maybe the novelty would wear off anyway if he could take them all the time?!
@Isthiscorrect unfortunately the school don't have a librarian, I'm guessing they just don't have the funds; they have a couple of volunteers who go in every so often to help out in the library, listen to the children read etc, but no permanent librarian. @missjonesy DS would absolutely adore going to a Lego club or similar but again, there's just not the opportunity, if there was a librarian he could perhaps have sat in there but the library isn't open at lunch time. I can completely understand about your school's lack of capacity @PutWoodInHoleDuck as ours is similar, they can't run many lunch time clubs as they have the minimum of staff, and after school clubs are run by separate companies and are usually chargeable.
I did feel a lot better after the chat with the teacher (as did DS) but we seem to have taken a step backwards after half term... sigh! DS is back to dreading break times. I may well suggest something similar to the nurture club @JaneFarrier as perhaps school could instigate that for minimum cost!