Sorry, deleted original thread about the Minor cutting out or not starting when warm.
My money is on the petrol filler cap. Had exactly the same problem years ago. Blamed the fuel pump initially, as it was seriously hot and famously unreliable (SU - similar to yours?). Had to abandon the car one night, went back next morning (surprised to find it still there, including wheels). Having thought about it overnight, recalled that I had managed to lose the filler cap when refuelling - God knows how - so bought a cheap rubber cap to do for the moment.
Anyway - next morning, having wondered about venting, went back to car and removed the rubber cap. Not so much an intake of air - more a mighty bang as the petrol tank resumed its original shape. Large hole bored in rubber cap with a penknife, ran perfectly thereafter.
Of course the reason the fuel pump was hot was that it was trying to do the impossible. A herring of the red variety.
So - next time it happens, just take the filler cap off and see if that solves the problem.
Good luck,
GMack