Never had an MGB but did have a TR6 all through the 70's and early 80's. The car never failed to start except one day at work when the circuit breaker for the outside plugs tripped and the car sat in -35 for 8 hours. It didn't like that one bit. 

All the talk of unreliable was just that with mine - Talk. It ran great but it did require looking after. And you can make these 50 year old ones pretty reliable with electronic ignition and better fuel pumps. It's amazing what an electronic point free ignition, electric fuel pump, electric fans will do for an aging British car.