The idea of a stand alone account with another organisation (preferably not in the same banking group) is a good one, I recently lost my wallet luckily, I was able to borrow money from a family member to get me through until the news bank cards arrived (longer than they should have as Nationwide messed up, despite being asked to cancel and reissue they just cancelled). I have since opened an ATM account where I will have an emergency fund with the card held separately from the rest so it will not be lost.

However with a different organisation is even better, hopefully both organisations would not hit problems at the same time.

In my experience Natonwide are just as slimey as the rest of the banking world, in my experience very few of them can be trusted, or care about their customers.