Victoria British and others sell an SU which is designed as a direct replacement for the Stromberg. It is plumbed to accept all the lines the Stromberg had. I think this is what is involved here. Either way, The problem is fuel getting past the float valve. It could be a stuck valve. It could be dirt in the valve. It could even be a sunken float. Any of these will result in the float chamber overflowing into the vent line and hence to the canister, where it becomes a short downhill trip to the anti run-on valve. The only other thing to check is fuel pressure. I gather that this car has had an electronic SU fuel pump installed. Pressure shouldn't be an issue, as these are manufactured to deliver the low pressures which are used in both Stromberg and SU carburetters. However, I'd be tempted to check it anyway. It shouldn't read more than about three and a half pounds, maximum.
From Lola to Land Rover, If it's British and has wheels, it's likely I've bloodied me knuckles thereupon