My mum has a house which backs onto a park, all the houses on that street and in fact every house which backs onto the whole park boundary have a gate in place for easy access.
What about your new street, do any of the neighbor have gates onto the park? Usually a good sign if it’s ok/nok.
The only time my old dad (RIP) got a call from the council was when he opened up the gap to make it wide enough to park his boat in the back garden. The council said there was no road access so he couldn’t do that etc. He said ok and put a removable section in the fence and left the boat there anyway. About right for my old dad 😆
Congrats on the new man cave BTW 8)