I contacted Apple Support, went through the tedious first-level escalation process, and eventually got someone who acknowledged the issue and that there is basically no way to turn this off at the moment.
The best they could offer was to complain through Apple's Product Feedback, so I've sent a "Bug Report" through the iPhone Feedback channel and would suggest anyone impacted by this to do the same, here are the comments I used:
It is currently impossible to disable the cross-app player controls on the lock screen.
These controls are permanently on the lock screen, evidently even when the phone is in my pocket.
On numerous occasions now, I've gone to get something else out of the same pocket, touched the screen and ended up jumping to a totally different point of the show I'm listening too.
Please see details here:
https://apple.stackexchange.com/questions/472851/remove-audio-controls-from-ios-lock-screen-bbc-iplayer-apple-music-spotify-e
https://discussions.apple.com/thread/255621763?sortBy=best