If you are selling goods to other EC countries and the customer you are selling to provides you with their VAT number then the goods will be zero-rated provided that the goods are sent to that country (UFS code EZG).
If the customer you are selling to doesn't have their own VAT number then the goods must be treated as if you are making a sale within the UK. This means that UK rates will still apply.
So, if you were selling a computer to a customer in France and they were unable to provide a VAT number you would have to charge VAT because a computer is standard-rated under UK VAT law.
If, however, you were selling a book rather than a computer, you would still zero-rate the supply as books are zero-rated under UK VAT law. However, you would use the UFS tax code ZR rather than EZG.