What age is it considered inappropriate to use the changing rooms for the opposite sex?

Nope, depending on when leisure centres were built will vary massively about how the changing facilities were designed. A few of my very local ones are Council ones built in the 70s. Generally, pools tend to follow the same best practice guidelines, which are for children aged 8 and up to change in the changing room based on their gender. Often, at age 8, children are allowed to use public pools (different rules for gym) without direct supervision of parent/guardian, so that sort of matches up too. Of course, there are other facilities that have different rules - maybe private or health clubs may have other age limits. Most in my area have separate male/female changing, but there is a move toward changing villages. The Supreme Court Ruling on gender will potentially influence this too- to make a shared space that welcomes everyone, and I think this would be a brilliant opportunity to make spaces more accessible for those with disabilities too. My young children (aged 4 to 9) are more than capable of changing themselves, but there is next to no chance I'd be allowing my sons in the male change without supervision. Even with their dad there, its still not ideal, especially with my young daughter as the male changing rooms are open plan without cubicles for showers/changing. At least in the female, there are cubicles, so there is privacy both ways. As other posters have said, it's about if my children could identify or react sufficiently to inappropriate behaviour from others. I know there are views that "things were fine in my day." But they weren't fine. Kids were abused and assaulted all the time. And if keeping my kids in the same changing room as me for longer protects them? Then that's a no-brainer to me!