For many years Tonbridge station used to have a very friendly station cat who was often seen meeting passengers on platform 3. The cat passed away a few years ago. A plaque has been erected and displayed marking his life. I am unsure if another cat has replaced him.
As discussed on the Island Line Upgrade thread, Brading is (was) frequented by a well-known cat, though he or she lives in a neighbouring house rather than the station.
We are all hoping that the cat is being kept safely away from the extensive engineering works going on to reinstall the passing loop, and will deign to return once the station returns to its normal tranquillity.
We had a tabby all the time I was commuting (2003-2015) - one that swanned around like he owned the place (typical cat then) and had a bad habit of sleeping in inconvenient places in the ticket office, or walking on keyboards while the morning shift were busy. That feels too long ago to be Sprout, although they look similar - but don't all tabbies look the same?
Todmorden station had a ginger and white cat called Dinky who used to live in the waiting room and had a bed next to the book-swap case on the window ledge. On warm sunny days he/she would stretch out on the platform - often dangerously close to the edge - but has now, sadly, passed away.