I’m no expert and have no experience on a MGTF to really help. However, it does sound a bit like no choke syndrome if it were an MGB.
Based on an ECU I had on a kit car it might be worth testing the cooling water temperature and air temperature sensor..
It is my understanding that an ECU is programmed to make the mixture richer for start-up when the cooling water is cold. It is or at least can be also programmed to enrichen the mixture for an initial number of revolutions of the crankshaft. Presumably that counting is achieved by the crank sensor and that must be working otherwise the whole thing would not run.
Be interesting to know what you find as the solution.