Our club uses a school's swimming pool. The dive school hire it for 4 hours a day on Saturday and Sunday and for 2 hours on Monday for club members. The legal position over here is pretty much the same - there is no law against it but no pool operator will let you rock up in SCUBA gear for the reasons mentioned.
We used to use a pool at a different school but we had to find somewhere else. The original pool was a bit grotty and the building was in disrepair. One day, part of the roof collapsed meaning the pool was out of action for a while. We managed to get use of the pool at a school that was built a couple of years ago and the facility is great. We decided to carry on using it as the old place had let us down several times - double booking us, arriving at the pool to be told it was closed for maintenance with no warning, billing us for public holidays when it was closed, and on one occasion telling us the pool is closed as there is currently a goat in the deep end (really!).
Most pools used by dive schools/clubs are either roped off or closed to the public. They don't want members of the public kicked by fins or prodded with snorkels. As spectrum says, there is the issue of having suitably trained people supervising. The operators of our old pool did not provide a lifeguard unless we paid for it, however, they did insist we had suitably trained safety cover. The new pool insist we use their lifeguard - usually a kid with no diving knowledge. It seem s a little OTT when there is usually a minimum ratio of 4:1 of trained rescue divers/instructors to students/inexperienced divers.