Interesting to read this because as a kid I watched these rigs rise into the sky as they were built then floated out. They're building wind turbines in that shipyard now.
Methil, which built Brent A and at least three other large platforms. As others have noted there were several other yards involved at that time, such was the size of the North Sea fields development effort. Some historical info here : http://hansard.millbanksystems.com/written_answers/1976/mar/...