Slightly biased here as I own a climbing wall, but generally kids aren’t mature enough to learn until they are around 7, which is why we generally don’t admit them to classes until then. Having said that I have taken mine semi regularly since he was 3, he generally climbs for half an hour or so and then wants to run around on the bouncy matting …….
So take them along, but you will have to supervise them (do you climb ?, if not you will have to go on an induction before you can take them)
Bouldering is easy for kids to do, but roped climbing does keep them in one place and you can always “assist” them over the harder bits.
The Academy is an excellent bouldering facility and a great bunch of guys. ( I live down south , so I have nothing to do with it !)