I can't find a website for it, but as close as I can find the Giant's Causeway and Bushmills Railway is £8 return for 2 miles. No fares available for the Downpatrick and County Down Railway either, due to flooding last November.
Looking further away from GB, how common is it for US preserved railways/roads to offer excursions rather than the public-transport-lite service? That seems to be the case for the Durango and Silvertown Railroad at least, with 5-hour excursions from $89 / £67 and 9-hour ones from $97 / £73 (which doesn't seem quite as steep considering it's for a line the length of the West Somerset and Welsh Highland Railways combined).
I don't think it counts as a heritage railway, but Interlaken – Jungfraujoch and back is CHF 99 / £88 with a GA Travelcard, CHF 112 / £100 with a half-fare card, CHF 148 / £132 with a Swiss Travel or Interrail pass, and CHF 224 / £200 without any discounts, for a journey which I think is about twenty miles each way. In other words, at least £2.20 per mile, and £2.50-£5 per mile for most foreign visitors. The most surprising bit of that to me is that, per mile rather than in absolute terms, it's cheaper than the Snowdon Mountain Railway.