The fare you found (£91.60) is available for purchase on board the Grand Central train (0942 from Northallerton & 1912 from London), but you can reduce the price to £87.50 by purchasing Advance singles on the same trains. Personally I do not think that the saving is worth it.
You want the cheapest? If I tell you the cheapest, which I calculate to be £69.90, will you actually take that route? I rather suspect not.
The cheapest combination of tickets, for a day return, amounts to £75.50. Are you prepared to gia Sherburn in Elmet, Bolton on Dearn, Netherfield and Grantham? The train must call at all those stations.
I see a lot of requests for the cheapest, but I am not sure that is what people really want, and it is rarely good value!
