I think that the 748 was called the Budgie by BA originallyOM15 I think that you are correct here.
I think it may have been given the name 'Budgie' by BA folks at GLA soon after its delivery when it would have be seen and compared on the ramp with the existing Viscount fleet. (perhaps also at ABZ & LSI?) The name certainly caught on and was often used by locals in the H &I area when referring their means of transport to the mainland!