Purchases from other EU states should be free of import duty and VAT (but buyer accounts for VAT in box 2 of VAT return and additionally box 4 if recoverable).
Purchases from outside EU in most cases carry import duty at rates dictated by the EU plus VAT at the appropriate rate. Unless a deferment arrangement is in place the duty and VAT have to be paid to HMRC before goods are released to the buyer.
If the supplier has a UK reg number then you treat it like any other UK supplier ie claim input VAT. The invoice must clearly show the input VAT.