I believe the V6 engines are built at Jaguar's own plant in the midlands, whereas the V8 engines are built in a Jaguar section of Ford's Bridgend plant.

 

Not quite right.
The AJ133 V8 and AJ126 V6 are both built wholly and solely at the Bridgend plant.
The 3.0 V6 diesel engine is built at a different plant, although I cannot for the life of me find which plant or where it is despite copious searching!
The Ingenium engine plant near Wolverhampton builds nothing but 2.0 I4 petrol and diesel engines at the moment but there have been rumours floating around for at least two years now that it will build 1.5 litre I3 and 3.0 litre V6 engines "soon".