DS7, saying he doesn't have any friends at school

[CandyCrush77]

Worried about DS1, 7, who told me last night that he doesn't have any friends at school. We were talking about a school club and i asked who his partner was and he said X then, "I got left with him because noone ever picks me." I probed a bit more and he said that noone ever picks him and each boy has a special friend they play with and he doesn't. I said, why don't you ask them if you can play, and he said that he does and they always let him but that noone ever asks him to play. He said that even after a talk at school when they had been reminded about the importance of caring for people (if you see someone alone in the playground, go up to them etc) noone still came up to him. I have also noticed that he doesn't get invited on nearly as many play dates as the other boys (he still gets invited occasionally but most boys seem to have them every week) and also not to that many parties. I specifically asked his teacher at parents evening how DS1 is socially and with friendships and the teacher said, he doesn't have a best friend as such (which can be a good thing) but that he is never without someone to play with. DS1 is quite difficult/prickly in temperament and does like playing alone a lot so I am wondering if that impacts. He can get quite impatient with me/other children and often isn't that likeable so maybe that is why he is not that popular. I tried saying to him, why do you think people want to play with someone? It's because they are kind, funny etc etc and you are all those things but you have to let them see your good side etc. but didn't seem to help. If I was being honest, if you are grumpy and difficult then people won't want to play with you but I don't want to make it seem like it's his fault and I don't know that he is not already doing that. Does anyone have any experience of this or ideas as to how I can help him? Obviously it's pretty heartbreaking to hear him say that. I have already tried with playdates (often don't get reciprorated and don't want to push friendships that don't happen naturally, plus I am at work and not there to faciliate to have to rely on our nanny) and I will obviously talk to the teacher to get his view but wondering what else I can do to help.

[Paperdolly]

Continue to invite school friends for play-dates. Let him join a club of his interest outside school to make different friends and gain a skill for his self-esteem.