Personally I would avoid the risk of using small "offshore" banks.
Nationwide offer euro accounts but you'll probably do better setting up the account while in a Euro country by calling into a branch. How well you can search for the best deal will depend on your language ability but remember that if someone is offering a much higher rate than everywhere else it could be because they are in a greater need of money.
My feeling is that you should stick to the larger national banks because of the extra protection/security. If you, for example, invest with Nationwide Building Society you'll be covered by the Bank of England guarantees but if you invest with Nationwide International the account will be governed by Isle of Man rules and the banking guarantees are less than for UK banks.