I am pretty sure that HST's used to request stop on the Cotswold Line between Oxford and Moreton ?
There are no request stops on the Cotswold Line.
Combe, Finstock, Ascott-under-Wychwod and Shipton were request stops from the late 1960s until the mid-2000s.
During the period the smaller stations in West Oxfordshire were request stops - though on weekdays the morning and afternoon 'halts' trains that served them stopped everywhere anyway, as there were always some passengers getting on or off - the booked services were operated by run-of-the-mill dmus, except between 2004 and 2006, when some of the Saturday request calls were in diagrams operated by FGW Class 180s, thanks to their selective door opening. On Saturdays you normally had to stick out a hand for a train to stop, or tell the guard you wanted to get off at one of the halts.
I think request stop status ended with the December 2006 timetable, when the Saturday services were withdrawn from Combe, Finstock and Ascott-under-Wychwood. Shipton was the only one of the four to retain Saturday services, all booked to stop.
HSTs did have some regular stops at Shipton on weekday evenings and Saturdays in later years, once FGW's HSTs had SDO fitted. This also allowed additional calls to be made at the other three - normally in late afternoon when the halts train back from Oxford had been cancelled and the following HST stood in to get people home - or special stops for Ascott-under-Wychwood villagers to get to Oxford or London and back for shopping on Saturdays before Christmas, that have operated most years since 2011.