Although it's probably never had a Rover (read Triumph) OHC 2.6 engine in it! I suspect this was one of the painted, and trimmed shells that sat outside the Triumph experimental dept waiting to go into the 2.6 engine development program but never got used. Quite a few of these painted, and trimmed shells (figures vary from 10 to 20'ish) subsequently got sold to those in the know in experimental for £250, bargain! These guy's subsequently built up the cars using existing identities from donor car's, or registered them as newly built cars. Some were registered long after Triumph had officially ceased production.
This car is probably one of those, hence it's 'flag of convenience' identity (standard 2.5 PI), further investigation needed on our part me thinks. The only clue to it's real identity rests with it's body number, but that means going through the Heritage archive microfiche car by car in the hope of finding anything useful (needle in a haystack!).