Yes, spreading the money around is a good idea as is avoiding "offshore" accounts and using banks that you know and trust. You may be limited in your choice by rules that state that certain accounts are only for people with an address in the country concerned. If it wasn't for that, there would be a very very large choice of accounts to choose from. Because of that rule, you may, in fact, be limited to "offshore" accounts. Offshore accounts on the Isle of Man are covered by some depositor guarantee while those on the Channel Islands are not.
Some mainstream UK banks offer euro accounts and that may be a better option than going "offshore". You should avoid anything involving changing to pounds and back to euros as every change will cost you money.