The National Conditions of Travel state:
"6.1. You must have a valid Ticket to travel before you board a train where there was the opportunity to buy one unless one of the following circumstances applies:
6.1.1. At the station where you start your journey, there is no means of purchasing a Ticket, either because there is no Ticket office open or self-service Ticket machine in working order; and where notices indicate that Penalty Fares may apply from that station, you purchase a Permit to Travel if there is a working Permit to Travel issuing machine at the station where you start your journey – see Condition 10 for more information about Penalty Fares;
...
In these cases, you must, as soon as you are reasonably able, buy an appropriate Ticket to complete your journey. The price of the Ticket you purchase will be the same as if you had bought a Ticket at the station from which you first departed. "
Clearly, if there is insufficient time to reach the booking office at Cheltenham, then you are not reasonably able to pay your fare at that point, so your first reasonable opportunity is the guard on the train north from Cheltenham. Indeed, whilst information boxes are not binding, the following information box backs up this view:
"INFORMATION: This means that you should buy a Ticket from the conductor on the train if there is one available; at an interchange station provided there issufficient time before your connecting service; or, if neither of these is possible, at your destination."
I would write back to TIL pointing out these facts, that you are contractually entitled to buy on board in these circumstances.