I doubt a 948 Mini would have done the 1963 RAC Rally as that would not be a homologated engine size in Groups 1 or 2, and thus not allowed on a European Championship international rally.
I serviced for 2 Coopers on the '63 RAC using a Vauxhall Victor Estate. What is the guy's name as I might well know him.
The first RAC I competed on was the 1964 in a 'semi-works' Simca 1500 - the worst, or equal worst, car I ever navigated in (the other load of junk was a Marina 1.8 TC Coupe)!
In those days the RAC was, typically, 2500 miles long and it ran from Sunday morning until Tuesday evening without a break of more than 1 hour on each morning, then from Wednesday morning until Thursday evening again with only a 1-hour break on Thursday morning. There were some long road sections where the crew would take it in turns to drive whilst on the special stages the co-drivers would read the road from the OS maps as no practice was allowed and all the stages were 'secret' and driven 'as seen'.
I remember in 1964 my friend Barrie (Whizzo) Williams rolled his Cooper 'S', 120MNP, a few times. Each time it got narrower and in the end, on a long road section, he found a body shop and got them to use a 'Porta-Power' to make it wide enough to sit comfortably in again, if a rally Mini can ever be comfortable

.