When I am away from base I normally have my own PC with me but, for the occasions that I do not - I use Phone Banking.
It might be more expensive as you have to make the call but most bank's phone access are open 24 hours a day. I try and call when it is night time in the UK, so that I get through quickly! Then I speak directly with the agent, get asked security questions at random and so forth.
I have used First Direct for 12 years, as they had the only international solution (i.e. with Voice) before the Web came along. I also use LLoyds TSB.
With international callingn cards, the cost is not too bad and is secure, not least as your call is tape recorded by the bank!