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 the particular country’s language, and it must be submitted with the original invoices. There is a useful H.M Customs & Excise booklet, VAT Notice 723 that covers the procedures.
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 for when VAT can be claimed, and notice 723 will give you further guidance.