Thank you to those of you with balanced responses that have brought some sanity to the thread!
I've taken on board the comments that I cannot simply disregard DP's feelings. Fair enough. He has misgivings that he cannot articulate beyond "it is not appropriate" but I'm not going to just ride roughshod over this feelings.
However, laying that aside, some of the attitudes and comments on here are perplexing and depressing to say the least.
I see people are still commenting on the dangers of the lift share, DD being the last one left in the car...once again the dad will not be driving. Everyone walks to the swimming pool.
I’ve been accused of being lax because I’m not supervising DD whilst she swims. She’s attending a swimming lesson so there is a teacher and a lifeguard in the pool. No supervision from parents required.
I'm reading that some of you have 9 & 10 year old children who cannot dry and dress themselves/feel uncomfortable doing so and I'm putting DD at risk because she "might need help". Help with what? I’ve never met a NT 9 year old who cannot use a a towel and put their own clothes on. KS1 Primary school aged children who attend PE and swimming lessons have to do this on their own as teachers cannot help 30+ children.
As I've already pointed out, DD has been to his house for play dates over the last 8 years. On occasion in the last couple of years we have left her there (birthday parties, playing after school with his son and other kids) which would have given him ample opportunity to practice evil deeds. Instead, many of you think it is entirely feasible that he is going to wait until he takes DD swimming every 3 weeks, find some pretext to go into the changing village and engineer his way into her locked cubicle and then attempt to abuse her with other children close by.
Alternatively I've also read that he might try to abuse her on the walk home from the swimming pool whilst the other children walk on ahead. I can't even fathom what kind of scenario that would involve 
I'm aware many paedophiles brazenly abuse children in plain sight and I'm not trying to make light of the very real and serious issue of child sexual abuse but some of the comments on this thread are ridiculous. I'm not even going to comment on the "I've never left my DD with a man apart from DH" except to say that level of mistrust sounds exhausting and stressful.