All commercial transactions (where you sell products in UK for profit) require an EORI (Economic Operator Registration & Identification) number.  This was introduced in July 2009 to minimise cases of fraud.  This is regardless of whether you are VAT registered or not.

The good news for VAT registered companies is that your EORI number will be the same as your VAT Number, but you still have to register to be EORI approved even if you are VAT registered already.

To apply, go to https://www.gov.uk/eori

If you are importing goods for your own personal use, and not for commercial sale, you need only state those words alongside the shipment details and then your agent will be authorised to bypass the EORI system and declare the goods for private use.

Of course VAT registered companies can reclaim the VAT they pay to HMRC and non-VAT EORI registered companies and private individuals cannot.