Silver Birch is the colour but just to cause confusion, according to my DULUX Autocolour book, there are 3 versions of Silver Birch .
BMC/Leyland 64-65 Silver Birch code 06968 Trim colour
BMC/Leyland 71-72 Silver Birch code 13260 Trim colour
Rover 69-70 Silver Birch code 12652. (NOT Leyland/JRA type Rover. UK type Rover?)
The formula shows the 13260 code to be a lot more metallic than the 06968 code. The 71-72 colour would seem to be the lighter silver used on Clubman cars. But then I'm no colour expert. Just looking up the book.
Between 65 and 71 ??????. Most likely still the 06968 code which is a darker silver/grey than the 13260 code.
OZ built Cooper 'S' wheels were a darker silver grey colour rather than a light silver colour. UK cars used OEW (Old English White) for wheels. At least on the early cars as the DOC says. Later UK MK3 cars? I think may have been silver.
Best to take a colour sample with you and explain to the paint shop about the 3 different Dulux colour codes.
If you are a real pedant the wheels were only painted Silver Birch on the outside. The inside was not painted in Silver Birch. I seem to recall they were either black or red oxide primer on the inside but I don't have a wheel handy to check the inside colour.
Hope this helps
RonR