Sorry if I misled but it's not how all Sprinters came about! Most of the Sprinters were built as they are as 2 or 3 coach units, based on the design of BR Mark 3 carriages (same as the 125 set coaches), but 35 of them got cut up to make 1 coach units, resulting in the narrower doorways at one end. It's some of the GWR ones which have been sent to ScotRail.
I read some of the history because these were frequently inflicted on us in Somerset and it was a bit baffling how anyone thought such a bike-hostile design was a good thing for Bristol: and the answer is they didn't, with these sawn-off trains originally intended for rural branch lines in the midlands and north.