The main obstacle, whichever way you count them and whichever area you're in, will be travel between the entrances. Leck Fell probably has the closest concentration but at an average of 36 minutes per trip you're barely scratching the surface compared to what "doing" a cave usually entails. SRT feels quick but it's rarely
that quick, so unless you're going to pre-rig 40 ropes you'd lose most of the time to rigging if you commit to SRT. Better to spend 15 minutes going in and 15 minutes out of 40 horizontal entrances, with 6 minute walks between them, unladen with heavy rope bags.
At first I was thinking of Mendip, because I had a similar challenge in mind for the abortive "Cave the Sun" event this summer. Here's a map I made for myself
"Cave the Sun" As many short, obscure caves as can be reasonably done in a single day.
www.google.com
That contains 37 entrances which I think could reasonably be done with a CSCC key and only a short drive between Burrington Coombe and Priddy.
Upon further thought, however, I think you may be better off in Chapel-le-Dale in Yorkshire and working your way up to Ribblehead. There are a lot more small caves that aren't yet marked on the CNCC website, which can definitely be "done" to the end in less than half an hour, and several of the more well-known SRT caves there have enough horizontal before the first pitch that you can feel like you've actually been caving and tick them off.
Wherever you choose, you're definitely going to want to scout the entrances before the big day because any delay in finding them or getting lost on the surface will screw up the whole thing.