I'll just dust off my anorak...
There was one instance in the 1970s where G-BJCB was issued to two separate HS125s (original and replacement) for JCB.
On G-INFO G-BJCBX is the original aircraft.
I believe the CAA decided it was too confusing and stuck to their guns after that as IRRenewal says.
What state is BZYZ's wing in?