Visiting me from the USA at present is my best friend with whom I started rallying in 1959.We got a new 850 Mini in 1961 and in 1963 I won a U.K. regional rally championship in it as a navigator with my friend being runner-up driver (he missed one event due to having a 'hot-date'!). At regional championship level in 1963 we were up against the 997 Cooper, Anglia 1200, Healey 3000, Sprite, TR4, etc, and we were competitive with them all. Of course, my driver was outstanding, especially in a Mini, and the way he carried the speed (what speed?) through the corners and the total smoothness of his driving was what did it. I guess we had about 38 bhp in that car (9NKP). We did borrow an ex-works 850 (16BOJ) for a couple of events (we have nice friends), but it was all done in 850 Minis.
Just accept that an 850 with reliability as a rally car will have around 40 to 45 bhp and drive it accordingly. There is little in the way of brakes, so you are not able to slow for corners - keep it like that and carry the speed smoothly at all times.
I reckon an 850 in pre-'60 class will be great fun and a potential winner.
