Friends of ours with three children moved from London to a nice small cathedral city about 20 years ago. Fantastic for the kids growing up, and enough cultural life for the parents to have plenty of choice. Not like 100 shows in any week, but enough to have plenty of variety.
A big thing was that, though there's so much available in London, it may take longer to travel across London than to come in from another town on a day-return. So most of the hundreds of things going on aren't really available without a long journey.
They could afford to live quite centrally, which helps, and near the station so they could easily get to London and other places.
They did lots of research to find exactly what they wanted.
As others have pointed out, a downside is that you need a car to make the most of the countryside.
As the kids grew up and moved out, the parents did consider moving back, but realised they'd got used to fresher air, less crowding and rushing, a generally more comfortable way of life. They still visit London every month or two.
I think it's worth a try, OP.