Anyone can stay at Haven or legal caravan sites. You book them online. They don't ask if you're gypsies on the booking sites. We holiday at caravan/camp sites. Never seen any 'no gypsy' signs.
Of course, there are rules to be obeyed. You have to pay for the stay in advance and if the park does not have a residence license, most don't, they are only licensed as holiday parks, then you cannot legally live on them all year round.
But even then, we looked into living in a caravan for good. What you do is buy in a holida park, then, for 10 weeks out of the year, you have to leave. We know someone who does this. They swap with caravan owners in other parks in the UK.
Perfectly legal.
You can live a nomadic life without breaking the law, you know.