I hopefully unscrewed the little panel in front of the engine to see if there was anything I could attack with my magic WD40. Nothing but the engine and a big fat plug. The plug was covered with a thick layer of dust and grease, so naturally I couldn't resist touching it, and discovered that it was very loose. When I closed the panel and started the engine it turned over immediately.
Loose spark plug then - apparently a common bug in the ET4, as my previous model pulled the same stunt while I was driving down the M1 one December night. Boy do I feel smug. I've narrowly escaped being thought an incapable female by burly garage mechanics who would have charged vast amounts for a call-out, and I got to work, hooray. I am a genius.
Now why couldn't I have been a genius last night and saved everyone a lot of bother?