Hi Rob
They did indeed build SD1 and P6 at the same time! SD1 had a complete new assembly plant built for it - well the assembly plant that was to have built the P8 actually. The "old" plant that had been built new to build P6 was then to be converted to build Land Rovers and Range Rovers. But, at launch, the small capacity SD1's weren't ready because Triumph were having trouble with the straight six which was to have featured in their replacement for the Triumph 2000/2500/2500PI. Rover's new small engine for the P10 which formed the basis of SD1 had been cancelled at the time that the Rover and Triumph projects were merged in late 1971. That engine was a 2.2 ltr DOHC slant four with individual throttle body injection giving 160 bhp. The capacity survived to give the four cylinder P6 a few more years because, of course, this engine was to have been built on the existing P6 engine line tooling.
So in the absence of the SD1 2300 - which was the intended replacement for the P6 2200 - the P6 line was kept open primarily to build 2200's (and 2000's for Italy). V8's continued to be built right up to the end of production, though. With the engine available and the line available, cars were built more or less randomly, perhaps as part sets were identified. Rumour has it that some of the last V8's had SD1 spec engines, although I don't believe there has been any physical evidence turned up.
Of course staffing was a problem. The P6 line became almost a cottage industry. When there was a parts shortage that stopped the SD1 line (this was the mid 70's!), workers were transferred to run the P6 line almost normally. At other times small gangs of "spare" staff would work on a stationary line working from car to car.
It's worth putting SD1 in context too. In late 1971 there were three cars being developed for production. P8, the high tech Rover UberSaloon aimed squarely at the Mercedes S class, although originally touted to start with a 4 cyl engine. P10, which was a Leyland initiated Rover project to build something less tricksy than P8 to take on the Granada head on. And the Triumph project to replace the 2000/2500. At the formation of the Specialist Division all three projects were merged / cancelled. David Bache's styling for P10 together with Spen Kings much simplified Rovr suspension won out to go forward. The Rover V8 was added as a top of the range engine to cope with the loss of P8 and the new Rover 4 cylinder was cancelled in favour of the Triumph engines. The Austin Morris penny pinchers were brought in to make it cheaper to build (primarily, it seems to me, by cheapening the interior) and the gearbox was sourced from Jaguar. Welcome to SD1!
Chris