I think BMC/BL asked for the Buick engine, it was spotted at GM on a walk about, and asked what it was. They bought the rights to produce it.
BMC/BL were, for some reason, incapable of producing a V8, though the Daimler 2.5/4.5 Hemi was a lovely piece of kit.....????
The first Buick/Rover V8 was used in 1967 in this model below, the Rover P5, P5B.....