I could only guess, but if the overdrive indicated it was British then just from looking at the box with what looks like a floor shifter I'd guess GM so maybe Vauxhall Cresta/Ventora if any of those had a floor shifter, or Victor FD/FE but I may be miles off. Have you looked for casting marks on the gearbox casing?
Ain't that a wondrously crude-looking linkage?