First Class Seasons on the Bedford-Bletchley Line

[googolplex]

I've just discovered that it is possible to buy a first class season ticket on the Bedford-Bletchley route, even though all the trains on the line have no first class accommodation.
For example Fenny Stratford - Bedford Stations has a first class season available.
The regular fares are standard class only, so why would this be the case?

 

[37401]

Did the 31s have a first class Mk2? maybe someone forgot to take the first class fares off the system when it swiched to a DMU

 

[googolplex]

If you're referring to the time between the discontinuation of the Mk1 DMUs and the introduction of the Sprinters (in the early 2000s) as far as I'm aware it was all standard class.