Yes. If the ticket (in this case GroupSave) you want is not available from a TVM▸ and there is no other means of purchase then you are entitled to join the train and buy a ticket at the earliest available opportunity.
Strictly, if there is a
PERTIS▸ machine or TVM at your origin station, then, to comply with the National Rail Conditions of Carriage, you must either buy a Permit to Travel or a ticket that allows you to make part of the journey, for all those travelling. These must then be exchanged, as part payment, for the actual tickets required as soon as is reasonably practicable.
In practice, this can be a bit of a faff, particularly onboard when excessing up a batch of TVM bought tickets to GroupSave.
Nonetheless, the strict legal requirement, where facilities exist, is to have some form of ticket, be that a Permit to Travel or part distance ticket,
before boarding.
From the
National Rail Conditions of Carriage:
3. Where the full range of tickets is not available
If you cannot buy an appropriate ticket for the journey you want to make because the
range of tickets that is available at the station from which you intend to start your journey
is restricted, you must buy a ticket or Permit to Travel before you travel that entitles you to
make at least part of the journey. Then you must, as soon as is reasonably practicable, buy
an appropriate ticket to complete your journey. In these circumstances, you only need to pay
the fare that you would have paid if you had bought a ticket immediately before your journey.
The price you will have to pay will be reduced by the amount paid for the ticket or Permit to
Travel.