We used the Dartmouth Steam Railway on Sunday just gone for a day trip to Dartmouth (we were staying in Paignton for the long weekend). If you get the first train of the day from Paignton (10am) and the last one back from Kingswear (5.10pm) you can have a decent amount of time in Dartmouth. I've used the Swanage Railway to visit Corfe Castle on a few occasions, as well as for a day trip to Swanage from London when they did the Wareham trial last year. I've also used the NYMR for a day out in Whitby. But I guess I'm a rail enthusiast rather than an "ordinary" passenger and in all these examples the trip on the railway was part of the fun rather than purely a means of getting from A to B.
The closest I've probably got to using a heritage railway as "real" public transport is when we holidayed in North Wales a couple of years back. We spent a few nights in Llandudno and then a few nights in Porthmadog and used the Conwy Valley line to get to Blaenau and then had a single from Blaenau to Porthmadog on the Ffestiniog. Again, though, using the Ffestiniog was part of the experience rather than the most convenient way of doing that journey.
The closest I've probably got to using a heritage railway as "real" public transport is when we holidayed in North Wales a couple of years back. We spent a few nights in Llandudno and then a few nights in Porthmadog and used the Conwy Valley line to get to Blaenau and then had a single from Blaenau to Porthmadog on the Ffestiniog. Again, though, using the Ffestiniog was part of the experience rather than the most convenient way of doing that journey.