I can say for sure that the Dunlop SP3 was THE tyre to have on a Mini for rallying in 1962 - 64. I always used them until the SP41 came along and the SP44 Weathermaster was introduced for loose/gravel roads.
The Goodyear and Firestone introduced their own 10" radials, the G800 and the F100 respectively. In fact, I was one of the test drivers for the Firestone F100 and the early 10" ones suffered from sidewall de-lamination so the design was changed very early on. Later Goodyear did the Ultragrip radial knobbly in a Mini size. In about 1969 the first 165 section Mini tyres became available, but the 145 was still considered better in the wet or on ice/mud or gravel.
How tyre technology has improved and today's Mini tyres are so much more capable. I always find it amusing when I hear criticism of current tyres like the Falken range. Compared to the early Mini tyres they are amazing!
I still think a Mini handles best in all conditions on 145 section tyres, even though the road holding in the dry may not be quite as good as with a 165.