Actually the Brits never had a false sense of security. It was exactly this vulnerable position at home which led them to establish a navy that during the general course of the following centuries had always the upper hand against foreign attempts to compromise this kind of british defence.
Its pretty much the same what the US are doing now with a navy that is far superior to everything potential adversaries can offer.
Terrorists CANNOT invade and seize a country. Yes, they may wreak havoc, such as with 9/11, but seriously: if you dont want to turn your country into some kind of orwellian nightmare, than there is no defence against such a threat from a security force-perspective.
Also this kind of damage (bomb attacks against public/commercial buildings etc) may appear horrific, but this is measured in peace time lifestyle-parameters. Just ask Germany in WW2 or maybe the British, French or Russians (esp. the Russians) as well, what kind of damage a terrorist attack like this would do to a nation that really is at war with an enemy. The answer is: zero/nada/nil. I admit however that this might get more complicated if the terrorists would get their hands on some kind of WMD, still contrary to all scenarios put up in the media etc. this seems not to be the preferred options due to reasons not completely clear to me. But the 9/11-incident is an excellent example of that.
Now guerilla tactics mean a strong support base from within and it is my impression that the current type of terrorist would finde more of that support in lets say Europe than the US due to different social environments. But maybe I am missing something here...
And of course you can put up a field hospital much easier in Iraq than in the US. In Iraq you have basically unlimited access and authorization in order to make things going. Iraq, contrary to what politicians might say, still is a warzone, with all the "benefits" of handling things. This is not the case within the US and its peace time regulations, rights etc. I am not saying the US gov couldnt have handled the Katrina situation better than they did. Still its rather useless to take Iraq in comparison. It would be better to look at other functional countries for what natural desaster relief mechanisms are in place there.