The GM alternators you were using were probably the 63 amp 10 SI. That still a far cry from the early Lucas alternators that put out about 35 amps. Alternators will put out anywhere between 30-50% of their rated output at idle. So, in the case of a TR3's 20 amp rated generator, that 10 SI GM unit can put that much out at idle.
Also, as a point of interest (or you can stop reading if you're not interested), when alternators are 'modified' to put out more amperage, very often the 'Y' wound stator is replaced with a 'Delta' wound stator. That will increase the output of any alternator, but low speed performance always suffers. Therefore, the new high amp alternator most likely will not put out as much at idle as the original 'Y' wound stator. What OE manufacurer's have discovered over the last 8-10 years, is that by rectifying the connector in a 'Y' wound stator, the total output will increase by about 5-10%, but still retain high low speed output. These alternators have eight diodes in them instead of the normal six.
Are you bored?? Ok, I'll shut up!