Chimevault my explanation above applies to B2C only.
B2B: No VAT needs to be charged if your customer is the importer of record (and it’s being shipped directly from you to the company in the UK). If you are located in EU or in U.S. and shipping directly to a company customer make your UK company customer pay the import fees to the mail office/shipping company. The company customer can reclaim this later from the UK tax authorities (they include it in their regular UK tax reporting). There are of course exceptions and also some companies may not want to be the importer for some reasons but those are my general comments.
Thanks again,
Bianca