This sounds AWFULLY familiar!! Without wanting to identify the guilty, would you be making a hypothetical situation from a recent real one?
Would FL180 in a single engined, German registered aircraft, a diversion airfield on the east side of England, and an ultimate destination not a million miles from an international airport in Northern England about cover it?
If so, I was the controller dealing with the emergency, and must say, as a pilot myself, that to take off again would seem a little rash. That particular emergency caused a lot of bells to ring, being single engine over the sea, at night etc. D&D and the approach unit and us in London Control were very concerned and I watched the radar trace all the way to the diversion airfield, giving range checks and distance to the coast all the way. Even when the aircraft was transferred to the approach unit, we continued to monitor to check he landed safely.
If you are now suggesting that he took off again... I begin to wonder whether all that attention was worthwhile. But of course we will always take emergencies like this seriously.
I was also party to another emergency a year or so ago with a single engined aircraft over the sea which reported EXACTLY the same fault as this one. When that one just made it into Southend, the engine stopped on the runway and the cowling was covered in oil....