Hello Peter and welcome.
As others have said, A/C is quite a rare option on a Classic Morgan; therefore, I didn't have the answer to hand. I did however call the factory and this was the explanation: -
There is a drainage tube for the A/C and it should be found to the rear of the heater unit - between the dash and the bulkhead. The tube should be the size of pipe you would expect to find for windscreen washer fluid. This tube should be attached to the rear of the Heater/A/C unit and should then travel over the top of the bulkhead and into the engine compartment. From there it passes down past the top of the gear box (bell housing end) and allows the water to fall onto the road beneath the car.
From the sound of it, the hose is missing from your car, hence the water dripping down behind the dash and into the footwell. The easiest solution would be to get the dealer who supplied the car to send you the appropriate pipe and fit it yourself, now that you know where it should be attached and the easiest route out of the car. You could also try to source some appropriate diameter pipe and follow the same process.
If you get stuck, let me know and I'll put you into contact with someone at the factory who can be of assistance.
