Hi Margaret and Ken,
Have you got a Manchester library card to access the Guardian and Observer newspaper archives? If so, do a search for 'White Heather camp' and 'Heaton Park'
I just did, and there is a piece dated 10 Feb 1917 that describes a 'hydrotherapy' pool at Heaton Park in 1917, used for the treatment of convalescing soldiers. I knew they trained the Manchester Regiment at Heaton Park, but apparently there was a convalescent hospital set up there as well. Its fascinating, apparently they had a sort of early Jacuzzi - in Heaton Park, in 1917! They were about to build an extension called the White Heather Military Hydro.
Could this be the origin of the swimming pool?
There's another article, 7 October 1916 about the hydrotherapy treatment, says there is a photo on another page of the paper but I haven't found it yet

If you can't find the articles, send me a PM and an email address. I'll try and make time to transcribe a bit of them later

Barbara