I believe there is no VAT or any other duty to pay.
"Importing from within the EU / EU Harmonised Import Tariff
The EU countries have a common harmonised import tariff - the TARIC. The UK import regulations outlined below are equally valid for all member states of the European Union. Furthermore, if you are importing into the UK from another EU country (or between any two EU countries) there is no duty to pay. The TARIC rates are set every year and published in each country - the UK version consists of 21 sections, 97 chapters and 14,000 sub classifications. As a result, this article can only give broad guidelines and comes with the proviso attached that any information given is for guidance only and should be verified with HMRC (HM Revenue & Customs) before being relied on". Taken from click here.