What ideally should be happening is that the car should detect that only one phase is available, and if the cable is rated for 32A, connect two 3.3kW on-board chargers to the single available phase (usually L1). The car can tell the current rating of the cable by a resistor in one of the control wires. Teslas and most other EVs with 11kW on-board chargers do this switching automatically.
I actually thought that MGs do this as well. So it's possible that your car's charging circuit is faulty (perhaps a relay is missing or its drive circuit). Good luck explaining the problem to your dealer, and getting it fixed under warranty.
But if MGs simply omit this circuit, a workaround would be to get your electrician to wire L1 and L2 both to the same phase, and use a 3-phase cable instead of the one you have now. It should not be a 16A rated cable, as the neutral conductor will be carrying 32A, even though two of the live wires will be carrying only 16A, and one will be unused (0A).
It will be interesting to find out if other MGs have the same issue. Would any owners with 11kW chargers care to comment?