This has long been an interest of mine, probably because I like to swim in my t-shirt!
Olympic star Rebecca Adlington has been promoting a policy designed to remove barriers to swimming!
"The policy will allow swimmers to wear tight-fitting garments such as leggings, short and long-sleeved t-shirts, and swim dresses. The guidelines are designed to make swimming more inclusive and tackle some of the barriers that prevent people from taking part."
I would suggest just asking. I remember asking the lifeguards at Stonehaven outdoor pool if my companion could wear her t-shirt over her swimsuit and they just said, "Yes!" Peter
There are a number of private pools around the Norfolk area that you can hire for the hour. We've looked at several for filming but the moment you mention anything out of the ordinary they don't want to know. Perhaps hiring it for an hour and not saying exactly what you want may be the answer, perhaps falling in and having a spare set of clothes. Rather than put links on here search private pool / swimming pool hire and you will see what's around.