It did not occur to me to buy train tickets in advance. Found out the hard way. LON to Bath Spa is 78 pounds one way without advance purchase. Several sites sell tickets in advance for as low as 14.50 pounds one way! My host told me about it and my return was much cheaper! She also said that some people just keep checking periodically and book it when the extra cheap tickets come up.Booking several days in advance helps. Booking several weeks or months helps too. I searched cheap tickets England or GWR.
What you are speaking of is a type of ticket called an Advance ticket.
They can be very inexpensive but they are only valid on exactly the train indicated on the ticket and are non refundable.
The train company operating the train, in this case GWR can sell these tickets, and you have a better chance with them than others for late specials, but any of the TOCs (Train Operating Companies) can sell any ticket to any destination.
There are also several third party ticket sellers, too, like Red Spotted Hanky and the Trainline. Those will also be the same tickets but they will add charges and shipping charges. And if anything happens the TOCs won't help you and you will have to go back to the third party.