Hi John,
I believe it was the Mid-Norfolk railway, as the map they showed on the programme had East Dereham-Thuxton-Wymondham
This linky on the MNR website also shows it...
http://www.mnr.org.uk/about/routemap/
(Now I've moved to Norfolk I'm thinking about volunteering as a driver on the MNR - as they have 37s
).
Hope this helps.