Austin Princess 2200
Hi, here's a couple of guesses. I am not familiar with that model but being '70s BL does it have an electric fuel pump which is at the back and has to 'push' the petrol to the front? If so, you may just have the fuel draining back and then it takes a few seconds to refill the carbs. If this is the case, you can try to hold the ignition on for a few seconds before turning the starter, if you have an accomplice, you may even be able to listen if the pump is buzzing at first, and then stops. If the motor starts then first go, that is the cause.
If not, I would be looking for a vacuum leak, inlet manifold, carburettor gasket or similar.
Like I said, I am no expert, but that is where I would start.
Hi not sure if you have fixed the problem,but that could be a slow starter motor problem and you will need a battery with plenty of charge.