Why is it that ds can swim during a swimming lesson, but not when we're just messing about in the pool?

[SixImpossible]

He's also bewildered by this.

In lessons he can float front and back, tread water, backstroke, doggy paddle and - almost - crawl (he can crawl a width, but hasn't quite got the breathing organised). Yet when we're mucking about all these skills go out of the window. He retains his underwater skills - surface diving, bellyflopping confidently duving, jumping, somersaulting - but not his surface skills.

What is going on, and how can I help him?

Given the choice DS (age9)would hang around my neck and be towed around my DH and I when we swim together. I can barely swim 2 lengths, DS is a club swimmer, achieves county times and has completed his 3,000m badge.
No idea why he wants to make out he would drown without me!

Because 'play swimming' is just that - for playing not what DS does in lessons.

During his lessons, is the teacher in the pool with him? If so, it might be because he's looking up at his teacher during the lesson. If he's mucking about with you in the pool, he's looking straight rather than up. Looking up will help him keep his head up for surface strokes. Don't worry, it will all come. Mention this to his teacher who should be able to give you some tips. If you're swimming regularly between lessons, you should be getting "homework" to practice anyway.

He needs to get the hang of it in the next two months. Based on how he appeared to be a strong enough swimmer in the lessons, we booked a summer activity that is only open to swimmers!

We're going to have to fit in more swimming practice, but I don't know how. The pool is taken over for swimming lessons weekdays after school, and in any case we have something on for at least one dc, if not two out of the three, every evening.

Don't panic. Keep going let him play he will build up his strength and you and he know he can do it as he can in class. Try not to test him he will pick up on your concerns. Try games like diving to get things off the bottom, chasing a ball or small floating object. Most importantly have fun and enjoy try not to worry.