I think that back in British Railways days (1950s) there were a number of maroon and cream vehicles, notably Bedford OB. I have a vague idea that they both provided a fleet to provide a rail replacement service when necessary (much, much less common then than now and often in an emergency) and for various tourist excursions. BR also seems to have acquired elderly secondhand vehicles for staff purposes, such as ferrying traincrew to and from depots when they were distant from major stations. I am not sure if they were also used to get PW staff to and from the site of work. (All this is from some very vague recollections.)
I can't state with certainty, but I think this is unlikely, and think there would be more photo evidence of them in action if they had been used by the public.
Firstly on the basis that the economics of having vehicles for emergency use and occasional excursions doesn't add up, even by the standards of nationalised industries in the post war years.
Secondly, on the basis that the railways did run their own buses at one point in time, but stopped doing this (I think there was government intervention) around the late 20s / early 30s, and ended up taking shareholdings in area bus companies instead.
I think it's more likely they were used for staff transport, either regularly to sites that were remote from the railway, and / or as required for permanent way maintenance staff. At that time, contractors (and schools, churches and so on) did not need to license vehicles / drivers or themselves under PSV law so long as they were only carrying their own people and not directly charging for travel. (the law on this changed some time round the late 80s / early 90s.)
The website 'Ian's Bus Stop' has quite a lot on all things London Transport, and the
fleet history of the GS type records MXX 383 (GS 83) being used at BR's work study training centre, Watford. (The Grove is now a hotel, about 3 miles outside Watford - originally taken in to railway use to move offices / office staff out of central London during the 1939-45 war.) The site lists MXX 338 - GS 38 as passing to BR, but no info about where it was used.
Old Bus Photos website records BR running a staff bus between Sheffield Midland Station and Tinsley Yard (at the time of the photo, an ex Mansfield District AEC Regal III
A search on Flickr comes up with 4 photos
by this user of Bedford OBs in BR livery (all seem to be parked up rather than running) but does not give any detail about where / why / when.
It also comes up with
this image, which is photoshopped, but refers to OBs being used as staff buses by BR.
www.themodelcentre.com