Mk2 seats (headrest type or non headrest) will fit a Mk1. The headrest type were facelift Mk2 seats from 1974 on. Purists will pull their face though as they will stand out as not being Mk1 seats!!!!
Repairing the original leather seats would be the best solution; if it's just the stitching that's perished then that isn't a problem as long as the leather is still quite supple and not hard. If the leather is torn or damaged you will not find an identical leather to repair them - the diamond pattern has not been available for a long time. Best bet is to buy a good used set, but be prepared to have a long search and to pay good money for them!
Firstly, Andy Harrison (Devon Group Leader in the Triumph 2000 Register) maybe your first point of contact as he has a good supply of used parts.......but don't hold your breath!
Secondly, if you join the Register
you may find useful contacts in the Club to help in your search.
Alternatively, you could sell me your car and save yourself the hassle.....!!!!!