Yeah, I think you're right. Where I lived, in Stevenage, the original A1 was renamed B197, although I wouldn't have known that at the time - only that while I'd been a passenger in the car, I'd seen both the A1 and A1(M) and signs to them fairly frequently.
I guess my teacher was right and my youthful smugness was unfounded and misplaced. :D
EDIT: I just googled a bit more and discovered that at least one map (the one inch map from 1963) labelled the old road as A1 and the new road as A1(M) as distinct roads on the same map. I doubt I'd have actually seen that though, as it was from well over a decade before I was born, although my dad had lived in Stevenage around that period so maybe he still referred to it by its old name and I'd just picked up on that. Or more likely, I was just wrong!