EC Global Membership simply means you do not 'reside' in one of the geographic locations where BA has dedicated EC programs.
In other words, the EC don't have a specific scheme for your chosen location, so they use a default scheme.
Your Service Centre would depend on where you live.
Generally it is not a wise option to enroll in the EC where there is not a specific scheme, as you are effectively barring yourself from targeted promotions.
Nick