There is a mention of Credit Default Swaps, which I admit I know nothing about, but the presentation of the story was strongly geared towards whether customers should be putting their money into banks like IceSave (aka Landsbanki) and Kaupthing. My own impression of the report was that a number of British banks are probably unhappy at the way they are losing custom (apparently UK customers have deposited £6bn in Icelandic banks in the last eighteen months). They are losing custom, of course, because these banks offer higher rates to savers. It's difficult to argue with that, so we have to muddy the water by insinuating that they might be less safe than a UK-based bank, though if it ever came to it, I rather imagine a Scandinavian regulator would be more efficient at paying out from the requisite compensation scheme.
Channel 4 News even interviewed a minister who parroted that cross-border banking needed to be regulated at an EU level. A fat lot of good that's going to be for an Icelandic institution.
The fact is, if you have more than £35,000 in deposit accounts in a single banking institution, you are rather well off and bluntly, the loss of that money shouldn't affect you in the short term (OK, there are edge cases such as people in the process of a house sale or purchase). Of course, that's not to say it would not affect you in the medium to long term. However, it is perhaps a sign that a wiser strategy would be to spread the risk across many institutions, or to use the money to invest elsewhere, such as in relatively low risk funds. A fund value may fall, but it's unlikely to vanish to zero. There is no such thing as an absolutely risk-free way of doing banking, and when trust and confidence are in short supply, there aren't easy answers.