you are allowed to fly your plane anywhere that is not specifically prohibited ie if the park does not have a no plane flying sign (rare these days) and you have the permission of the landowner. So even if the park allows plane flying I doubt you'll ever get the local council to give you permissioin.
However modern park flyers can 'fly under the radar' so to speak.
I sometimes fly in a local park, but make sure that there is few people using it ie no cricket, or soccer training. I've alao flown in a park a bit further away where a no flying sign went up (without any notice). The local ranger stopped us from flying but did let us know where we could fly.
If you want to take a risk (either you have enough money be sued or have no money so suing you is of no purpose) then fly without a club
If you join a club you get insurance that covers you even when flying at other than the club field. You'll alao meet like minded people who can help you.