Just realised the EGR valve is probably stuck 'open' - so compression was being lost down the exhaust, stopping the engine from running. Surprised it started at all, even though it was brief and wasn't happy, but does that sound right?
If so, I'm assuming it'll probably be fine to drive. When I think it through logically, all that will happen is the car will run slightly hotter (no inert 'cooling' hot gas present, haha), and It might flash an error code up once it's warm as the EGR won't be in the position the ECU expects it to be, so will trigger an error code / return to dealer message.
My question now is: Does the ECU close down the engine if it detects the EGR is not in it's expected position? If so, I can't drive it and risk it happening. That may also explain why the car is starting but then shutting down without the blanking plate.