Just to be precise and to correct the record in the hope of mitigating the negative effects of bad information being passed around the Internet, the wide ratio transmission used in MK II Tigers was the HEH-CF, not HEH-B as is commonly thought and published in some places. This is easily verifiable by consulting reliable sources, such as TIROST and/or The Book of Norman for MK II transmission numbers. Corroborating, proof in the pudding information can be had by crawling under MK II Tigers to look at their transmission tags.
To be clear, the HEH-B transmission had the same gear ratio as the Sunbeam Tiger MK II, but was not used on the Sunbeam Tiger MkII from the factory. In fact, the HEH-B transmission was used on the 1964 Meteor and the Fairlane 289-2V. It did have a wide 28-spline shaft, which made it easy to use on the Tiger, and I think it may have also had the correct-length tailshaft housing, making its transfer to the Tiger even easier.
Still, the only correct transmission for the MK II Tiger is the HEH-CF, according to factory records and experts. The only other car I know of that the HEH-CF transmission was ever originally used on was the TVR Griffith, which make this transmission truly as rare as hens’ teeth. Cheers.