I've lived in the Exmoor National Park, before I was farming, then farmed in the Northumberland National Park (and with a Site of Special Scientific Interest), then in the Hadrian's Wall World Heritage corridor (also AONB and with an SSSI) and now in an Area of Outstanding Natural Beauty in North Cornwall.
Planning is the biggest impact. The Park Authority has the major say in planning applications, and sets the planning framework. Much more rigorous about extensions, new builds, the look and materials, etc. On the plus side, we had no ugly pylons
. Yes expect prices to rise over time, and locals to get squeezed out by those price increases, resulting in houses empty during the week, local shops struggling except in holiday season, and so on.