thanks everyone for your thoughts. I did ring my local borough Council and the general gist was: if a road/car park is patrolled by a parking attendant on foot then it’s likely that the disabled badge in the windscreen is all that is required. If it is monitored by some other means (I presume CCTV) then you need to use the app.
As others have said, never assume. Always check the signs every time you park. I use Apcoa car parks occasionally and have registered for a blue badge online permit, but they make it clear that free parking for blue badge holders applies at most, but not all, of their car parks and you must check the signage at each location. It’s a minefield and making an incorrect assumption is likely to get you a parking fine!