OP It can be lovely but - as others have said - legally it can be quite complicated. You do need planning permission and you need to be able to prove adequate sanitary arrangements.
We lived in a caravan - officially - while our house was being built. It was fabulous in many ways - just step outside to the grass and the flowers and the wildlife (but also the mud in winter). But caravans have very little insulation. As other have said, they are cold and - much more important - they tend to be horribly damp. Clothes, towels, bedding etc can so easily get mildewy. Also caravans have very limited storage. Just think, where are you going to store clothes/ towels/ bedding? In winter, where are you going to hang up dripping waterproofs/dry out muddy boots? How - in a damp environment - are you going to keep clothes and bedding aired and dry?
Cooking, washing/showering and just breathing create an awful lot of condensation. Books and papers - unless stored in sealed boxes - are in danger of rotting. Black mould - very bad for respiratory health - is a threat. (I got a really, really nasty chest infection.) If you're serious about this, an efficient dehumidifier is an absolute must, and for that you need electricity. Bottled gas for cooking etc is very expensive.
You also need to think about where to put a washing machine (needs solid ground to stand on and a link to some sort of sanctioned drain) and a freezer. We had a shed for this - with planning permission because our house was being built. But in certain areas, without pp that would certainly not be possible.
As others have said, you need to register an address for schooling, GP, banking etc - and to pay council tax.
In many ways, our time in the middle of a field was wonderful. But it wasn't easy.