Below is a summary of how VAT is treated with links to the relevant guidance at HMRC.
Sales to customers outside the EU: If you are making supplies of goods to customers outside of the EU - no VAT is charged. The transaction is deemed "outside the scope of EU VAT".
However – exporters must keep accurate records of their exports, including proof of export. Please see section 6 of VAT notice 703 - "VAT: Export of Goods from the United Kingdom" for further information, including what is required as "proof of Export".
Sales to VAT registered customers in the EU: If you are selling to organisations in the EU that are registered for the equivalent of VAT in their country, then you do not need to charge UK VAT - your customer will pay their rate of VAT on acquisition. However there are some guidelines that you must follow in order to do this, including putting your customers VAT number on the invoice: ttp://www.hmrc.gov.uk/vat/managing/international/exports/goods.htm#1
Sales to non - VAT registered companies or to individuals in the EU: If you are selling to individuals, or companies in the EU that are not registered for VAT, or companies that cannot provide you with a valid VAT number, then you must charge the prevailing rate of UK VAT: http://www.hmrc.gov.uk/vat/managing/international/exports/goods.htm#2
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