I would say many if not most high street travel agents in towns would do train tickets in the 1980s. Can't recall if the big chain travel agents always did (eg Thomas Cook - tho they certainly stocked the continental rail timetable*) but independent locally owned travel agents were a common thing in those days - or perhaps a small independently owned chain with shops on high streets in several local towns. And every town would have a travel agent.
I suspect the one in Victoria Street might have been after a slice of the continental train ticket sales market, and if you were trained to do that perhaps you may as well sell BR tickets too as the systems were probably not that different.
* Got my 1st Continental Thomas Cook Timetable probably in 1990 or '91 from a Thomas Cook branch. On asking for it the lass at the desk (focussed on selling package holidays as 90% of her job I'm sure) looked blank when I asked for it, but consulted a colleague who thought she had seen 'something that might be one of those' out the back, which was duly located and happily sold to me. It clearly did not warrant shelf space front of house with the holiday brochures (but to be fair they would have been give aways and the timetable was not free).
Just realised -
did you mean BR high street shops as in shops on high streets operated by BR?
I think these were unusual - but I recall reading there was one in Brighton. Yes - here it is mentioned on the excellent 1S76 site:
So that must have meant BR operated a travel centre in the town, as well as the one located at Brighton station. I wonder how common this was? I would tend to think it would only happen in places with notable tourist business, or perhaps in cities with a business travel customer base but where the station travel centre was not conveniently located for the business staff (secretaries or clerks I suspect) to go out and buy tickets on behalf of senior colleagues planning to travel.