itsa,
Stiffer shocks won't really do it. They may initially resist lean, but that is only for an instant. Once you are in a steady state turn, only the springs and bars determine the height of any one corner of the car. This, in turn, determines the roll characteristic and the over/understeer. Shocks have only one purpose. That is to damp oscillation.
I have seen add on rear sway bars for the MGB before, but I note that Moss no longer carries them. I wonder why. Anyway, it CAN be done. Google around a bit and see what you find.
Motorbill
From Lola to Land Rover, If it's British and has wheels, it's likely I've bloodied me knuckles thereupon