Evidently not all Cortinas converted by this shop used the unusual roof and deck treatment of the puzzle picture.
On a Cortina blog there are pictures of both the puzzle car and another with standard roof, both by Crayford Auto Development Limited.
Details are: 3 litre Essex V6 engine and gearbox from a MkIV Zodiac.
I'll guess the puzzle picture is of an early development vehicle prior to 1968.
Attached is the 68 I found online.