OK - I see what you mean. There's the Marriott's Way... but that follows an old train route from Norwich to Aylsham, so I doubt that's be it?

Venta Icenorum (Market of the Iceni) at Caistor St Edmunds (also not for from Arminghall Henge) predates Norwich by quite a few hundred years, build by the Romans after Boudicca's revolt. So I'd guess that a link with the Peddlar's Way may have originally led there?

When part of what is now Norwich was established by the Saxons at Conesford down by what is currently ABC Wharfe on King Street (and the site of some kicking parties in the lock-ups!), it was said that a Roman Road passed nearby... possibly from Caistor St Edmunds along the course of King Street/Tombland/Fye Bridge/Magdalen Street (foundations of a very old timber bridge were found during excavations at Fye Bridge).

It is said that there was a crossroads where Tombland and the Cathedral currently stand with another road possibly following the course of Bishopgate. The medieval Bishop Bridge is built on the foundations of an earlier ford. Maybe one of these old roads could link up with the Peddlar's Way somewhere?

I also know that an old Roman road crosses the land on which Whitwell Hall near Reepham now stands and sometimes they followed older routes.

I'll have a bit of a hunt around tonight n' see what I can find on the maps... I'll let you know if I find ow't.