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There are too many differences such as shift cable, electrical hook ups etc. to use the BW8. It's not just a matter of bolting up.
This will answer your question:
Auto Transmission Application Guide
DG250 Three-Band: XK-140; XK-150; MKVII, VII, and IX; MK I;
MKII 3.4 up to VIN 181428; MKII 3.8 up to VIN 224737; 3.4S to
1B.26240; 3.8S to 1B.80287.
Borg-Warner 8 (cast iron): E-Type series I & II; 420; 420G; 4.2
MK X; XJ-6 Series I to engine 7L.8163.
DG250 1950 - '67
BW8 1968 - '72