Most councils have some sort of blanket ban bye-law, although they cannot stop you flying over their land (like they cannot stop BA flying their passenger jets doing the same).
It’s sometimes worth while to have a look a your local newspaper/online to see how many folks have been charged with breaking drone rules (the press love that sort of thing)
I filed a FOI request to North Yorkshire Police about this time time last year to see how many drone related incidents they had been called to, perhaps ask Thames Valley the same?