You may have your As and Bs mixed up. The MGA front suspension doesn't use the same kind of king pin and bushings as the B. It uses threaded upper and lower trunnions and a swivel pin that's threaded to match. No reaming is needed. You need to check for sloppiness in the trunnion/swivel pin fit. If they are indeed jiggling about, you'll probably need to replace both. This is neither cheap nor easy, needing a pretty hefty shop press, heat, and a lot of patience in most cases. There is an alternative.
You could convert to an MGB setup. You must have a set of shocks converted, (World Wide Auto does this by rebuilding a set of A shocks with a set of MGB arms, oddly enough, mounted upside down! and use different lower A-arms (the negative camber units offered in the Moss catalog) The neat thing here is that the MGB kingpins are demonstrably stronger, all the MGB suspension mods can be used, and the MGB Brake discs and calipers can be mounted with no further modification (after all, they are mounted to an MGB suspension) MGB calipers, and brakes in general, are much cheaper to service, and the parts are far more plentiful. Just a thought. It's the way I'm going on my "period bad boy sports car MGA" project machine.
It tends to sound complex, but it's really not. I bet if you go to one of the exclusive MG forum type sites it's been layed out chapter and verse by someone, complete with pictures.
From Lola to Land Rover, If it's British and has wheels, it's likely I've bloodied me knuckles thereupon