To insist DD has her own cubicle (or one with a friend?)

The simple answer is to get or adapt a towel. Some children (either sex) are self concious by this age as hormones begin to change.

The pool logistics will be down to staffing and facilities. Changing time is limited by a sucession of schools coming in and out and often bus timetabling. There isn't time to allow a sucession of children to take turns to use a limited supply of cubicles.

It tends to be difficult to have an appropriate male to supervise boys. Changing will be arranged due to numbers, pool protocol and supervision needs. It may be more practical to manage the boys safely paired up in cubicles rather than a more communal space with very limited supervision as it's difficult to balance their privacy/ safeguarding and supervision with staffing of the opposite sex.

I don't really care the reasons may be. Nobody should be forced to get naked in front of a group of people they're not comfortable with.

My boys have change towels. From decathlon that they use when body boarding on the beach

There is unlikely to be enough changing rooms to allow this. There is also a possibility that the pool allocate them a group change to keep the changing room usable and free for other swimmers. Yes, you would be unreasonable to insist on this. It is also excessive to be suggesting you will come over to get her changed. In your place, I would be explaining the reasons for the group change. I would also be telling her that no one will be looking at her especially as they will be busy getting changed.

I was going to agree until I realised it was a public pool and the school have no control over the facilities.

I agree with the suggestion of going already in swim suit and changing back under big dressing gown as someone else suggested.

It’s understandable for your daughter to feel self conscious getting changed at that age. I went to secondary in the 90’s and we all had to line up in front of a big walk through shower, one p.e. teacher at one end would pull the towel off you, you would literally run through as fast as poss barely touching any water and another teacher at the other end would hand the towel back. If you were any slower they would send the next girl in behind and you wouldn’t be able to look each other in the eye for the rest of the day. We all found it bloody awful. The stopped it the year we left and built cubicles.

These:

towellingwraps.co.uk

Easy to make with 2 towels and a bit of elastic. Can be made with or without arm holes, but if for getting changed it's actually better without IMO.

If no sensible resolution with the school, I’d consider withdrawing her from swim lessons and state the reason why. Escalate to the governors if required.

If they have access to 6 cubicles and there are 25 children in the class and each takes 4 minutes to get changed then you are looking at 25 minutes before and after each class for every student to get changed.

It makes sense that the same sex kids as the teacher changes in the bigger room under towels for privacy and the opposite sex kids get the cubicles. Swimming is an essential life skill and not all parent can afford or take their kids to lessons so swimming is school is important. I would hate to see it stopped because parents are complaining about all kids need their own cubicle or the school is violating their rights.

Why not just get her something like a changing poncho that can double as a towel?
www.amazon.co.uk/Dreamscene-Microfibre-Childrens-Swimming-Changing/dp/B092W61NZV/ref=mp_s_a_1_5?crid=35P0BWSM5HHTB&keywords=kids+changing+poncho&sprefix=kids+changing+poncho%2Caps%2C237&tag=mumsnetforu03-21&qid=1645647039&sr=8-5

Having supervised lots of children getting changed at swimming pools over the years as a teacher, it’s probably for purely practical rather than sexist reasons.

I think you be much better off finding a good towelling coat or towelling poncho because likely the school just won’t be able to accommodate your request.

Unfortunately even so young there have been occasions where some of the boys in the class have asked girls to show them their boobs when getting changed for PE. None of them have boobs yet but that's besides the point.

I assume this was swiftly dealt with by staff.

This is a really difficult one, the sports centre my son attended with school was the opposite issue.

There was a communal girls changing room but lots of cubicles that the girls were allowed to go in as there was sufficient rooms for each girl. However in the boys changing rooms there was not enough cubicles and a couple of the boys felt uncomfortable getting changed in the communal room (including my son). I spoke to school about it and they said as there was no additional needs they couldn't let them use the cubicles because if every kid might want to do the same if they see others using them.

I ended up buying him a poncho towel, he wasn't too impressed with it but preferred it to the alternative.

To clarify, you think it’s unusual that a teacher might not be comfortable seeing children of the opposite sex naked unless they’re secondary school age. Seems a little odd to me.

I completely agree that your DD shouldn’t have to change communally if she is uncomfortable but please don’t make out it’s odd for the female teachers to not be comfortable seeing male students naked. I would assume you would not be happy for a male teacher to see your daughter naked.

My DD8 is the same, feels uncomfortable changing in front of others. She’s a regular swimmer so I invested in a towelling dryrobe (sorry if one has already been suggested) It’s huge so will hopefully last a long while but being so oversized also means that it’s nice a long so she really can just remove her arms and change completely underneath it. Certainly sorted the issue for us ☺️

Maybe just maybe it is female member of staff supervising the boys hence the need for them to use cubicles.

Are the boys on the male changing rooms and the girls in the female 1’s?

Get her to wear her costume under her uniform to go and teach her to pull her skirt on and wrap a towel round her top and roll her costume off underneath it.

My DD had this issue in year 5 and ended up being exposed half naked to the boys in her class (largely due to lack of supervision and a spiteful girl in her class who thought it was hilarious to shove her though the door into the part the boys were changing in with only her knickers on). Above was my solution.

Somebody mentioned a tankini. Only full swimming costumes are allowed. I remember as a child feeling the exact same way, unfortunately they can't make allowances for one child as then that is obviously unfair treatment and would have to make allowances for all. I think it's just part of growing i'm afraid, I'm not sure it's something that can be respected. Either that or don't swim.

It's probably a numbers thing. My friend was chaperoning a dance show and one parent asked for her child to change separately. It meant that one child took half of the helpers for the group. Have they asked for parent helpers? I think you should volunteer if so.

Get, or make, a changing robe - basically a giant poncho made of beach towels, that's what I did for my kids.