Some tickets priced by GWR allow travel on certain trains and not others during the evening peak; this is encoded electronically in the manner in which you saw on the BRFares website. The key thing is though, that if you simply book an itinerary online you do not need to know anything and can simply catch the trains as per your contract, the same as you would a coach, flight or any other form of transport.As the OP, I thought I would follow up on a few points.
First, looking at the small print on the BRFARES website suggests there are small windows that allow the return ticket to work. Indeed there are two other return trains which although nationally at 'peak' time seem to allow this. The GWR site seems to suggest this is true.
The fact you had an itinerary is evidence of a contract.
Arguments can occur even when booking with GWR but yes GWR do appear to be acting in an anti-competitive manner ; GWR are opening themselves up to legal challenge if such behaviour continues.Second, it would seem prudent to book through GWR to miminse arguments. Although this strikes me as encouraging the anti-competitive stance of the ticket inspector.
GWR customer services are rubbish at resolving issues like this; it very much does need to be escalated. I'd be asking the retailer to support you too (a good retailer will do this).In terms of getting the money back, GWR have not responded to the details the posters here have provided yet. So thanks for the suggestions on how to escalate.
It's also worth contacting Barry Doe of Rail Magazine.
Heyford is outside London Travelwatch's area but the general principle applies to the Slough to Paddington corridor which they do cover, so it may be worth contacting them.
Transport Focus are useless, as is the Ombudsman, but you could try contacting them anyway. If nothing else I'd be interested to hear how they respond.
And as I said before, report a breach of consumer law to the ORR and remind them that they are required to investigate consumer law breaches.
The problem of course is that GWR have created a lot of work for you. Some train companies know that they can mistreat passengers because most people will give up and stop appealing/fighting. It's not a level playing field.