Not sure. My Matchless is a bitsa - built as a trail bike with an AJS engine. The Jampot dating officer (really helpful) searched the AJS/Matchless archives and provided dating info for the engine and frame since while they were both 1953, the bike did not leave Plumstead with an AJS engine in a Matchless frame.
The DVLA took this info, plus photos and my explanation and evidence of purchase and searched their database and found the original registration for the frame as this takes precedence. They were not in anyway interested in how the bike looked, only that it was a bike not a basket. Only complete vehicles can be registered, not piles of parts. At the time of registration it had no wiring.
Its important to maintain historic status so there must be "no major modifications" but for an old bike this would mean the same suspension, an in-period engine of a similar type and fuel, similar style. For cars points are allocated so its still allowable for several major changes. For a bike i can't envisage what it would take to loose the historic status. Some safety improvements are allowed so better brakes usually don't count as a mod.
The bike need only be within the range of the "specials" currently on their original registrations, that leaves a pretty wide choice. So if it has an alloy tank, rear-sets, single seat etc this would only make it like (say) 500 other BSA's on the road that still retain their registrations and historic status. To set a higher bar would be unreasonable and unenforceable.