We visited a cathedral 'darn sarf' last year and were pleased to see that they didn't demand anything. Instead, they politely asked if anyone would like to contribute and suggested a suitable amount. From what I could see, everyone coughed up without question.
Even I paid up perfectly willingly despite being, like you Tony, a 'tight-fisted Yorkshireman'! (Sorry.)
Needless to say, I thought it far more friendly to do things that way than demand a set admission fee and I wonder whether the overall income might be higher when asking politely. 'Demanding' certainly rubs up many people the wrong way, myself included.
In case I didn’t make it clear, the recital I sponsored was not at Coventry. I have no idea what cathedrals or concert halls (like the Bridgwater Hall) might charge for the use of their organ for a commercial recording - presumably a one-off payment in lieu of royalties? We must not stray too far from York, which was the subject here leading to discussion of admission charges, but it does highlight a problem for other cathedrals as well.