When Richard Gombrich taught the Sanskrit BA course at Oxford, Sanskrit composition was an option on the syllabus. In the finals, one could choose Sanskrit comp., or instead a longer unseen translation (if I recall correctly).
I think Skt. composition formed part of the syllabus under Burrow, before Richard, which would take it back to the war. I expect before that, it was also there, Sanskrit being taught on the model of Greats.
I don't know about the present syllabus.
Best,
Dominik Wujastyk