Why do I need a GB EORI number as well as a BE/LU EORI number?

A GB EORI number proves you are authorized to import goods into the UK. You can obtain this authorization by requesting a GB EORI number in UK:  https://www.gov.uk/import-goods-into-uk . A BE/LU EORI number proves you are authorized to export goods outside of the EU. You can obtain this authorization with FOD Economie (Belgium) and portail des Douanes et accises (Luxembourg).