No, in Belgium this is forbidden by law. Moreover, it is a really bad idea according to research carried out by ILVO, the Institute for Agriculture and Fishery Research. This research shows that eating 'wild' mussels can cause stomach - and bowel infections since they contain a high amount of microbes that can make you ill. Mussels picked off the beach or quay walls also contain more chemical substances than those you buy in the supermarket.
More information (in Dutch): http://www.ilvo.vlaanderen.be/NL/Pers-en-media/Alle-media/articleType/ArticleView/articleId/1815/Wild-geplukte-mosselen-op-Belgische-strandhoofden-en-kaaimuren-voldoen-niet-volledig-aan-voedingsnormen
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Animals at sea
Rules at sea