Got a 53 reg 1.6 Ford Fusion, it has an intermittent starting problem that occurs maybe once per week (it does about 25 journeys per week so most of the time its fine). When you start the car the starter spins up and turns the engine over, and then at the point the car would normally fire up the starter disengages itself. It will do this repeatedly until you prod the loud pedal whilst starting it and give it a good rev. It will then fire immediately. (I thought modern cars disabled the accelerator pedal whilst the engine is actually cranking to prevent abuse)
It does it both from cold or warm, I don’t think its battery/earth related as the starter spins fine, and 90% of the time it will start with no problems.
I’ve done a full service including fuel filter, only possibility is it needs new spark plugs but I don’t know if they would cause the symptoms I’m getting.