...........The pc in question has now been scrapped..............
Please clarify.
Was the Win 7 still installed in the computer when it was "scrapped ?
If yes, the answer is : no
Reason : as far as MS is concerned, that Win 7 product key is still in use. As such you cannot use the same key for another install to another computer.
On the other hand, if you had managed to uninstall Win 7 from that Vista computer before it was scrapped, then the Win 7 product key is free to be used for next install.
.......... one product key, one install.................