Only VAT charged by UK companies can be claimed on your UK VAT return. In order to claim the VAT paid in various member states, you will have to submit a claim form in the country that you incurred the expense. A special form must be completed in that country’s language and must be submitted with the original invoices.
There is a useful HMRC booklet, VAT Notice 723 that covers the procedures you must follow to obtian a refund of VAT in various EU member states.
If you are dealing with a number of EU countries you may find it advantageous to register in one of them and thus, subject to certain conditions, claim back the VAT for all the countries. You need to be aware that the countries involved do have differing rules on what VAT can be claimed on, and notice 723 available from www.hmrc.gov.uk will give you further guidance.