Marion locksmiths cut to code.
I usually just rekey the locks to whatever key I already have, it's very easy, minis seem to only use three in sizes in their locks. however if you know your code its probably easier to get a key cut than to pull your doors apart.

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The fleet:
1949 Fiat Topolino
1965 Morris 1100
1966 Mini Van (project)
19?? Morris 1500 (for sale)
1979 Chrysler Regal
1990 FSM Niki

Wilmot Breeden still exist (sort of), this is off their website

‘FS’ Key Series
These distinctive ‘hexagon’- headed keys are cut on one side only (‘single-entry’), and fluted on both faces so that cylinders resist screwdriver entry. The range has 80 combinations (‘differs’) from FS 876-955, which can be extended to 180, maximum. This is our standard series for handles and small locks and cannot be master-keyed. Keys can be ‘coined’ with a logo when volume is sufficient.

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1951 Morris Commercial J Type Van
1955 BSA C11G
1961 Morris Mini Traveller
1969 Triumph TR6R
1977 Leyland Moke Californian

#4 looks like a petrol cap key (after market) and #5 looks like a Krooklock key.

My 62 Cooper had one like #2 for the boot, don't know if it was original.

Pete