If you are not going to use this validation rule for multiple counties than no sense to use CASE function. Use ISPICKVAL instead

AND( 
    OR(
        LEN(BillingPostalCode) > 9,
        LEN(BillingPostalCode) < 6
    ),
    ISPICKVAL(BillingCountryCode, 'GB')
)

If you are not going to use this validation rule for multiple counties than no sense to use CASE function. Use ISPICKVAL instead

AND(
    ISPICKVAL(BillingCountryCode, 'GB'),
    OR(
        LEN(BillingPostalCode) > 9,
        LEN(BillingPostalCode) < 6
    )
)