You are right; the absence of support for the British Conservatives is puzzling, particularly given both the disillusionment with Blair and the resurgence of support for conservative, or at any rate right-wingish, parties elsewhere in Europe (Italy, Spain, Denmark, possibly Germany). None of the more common explanations seem very satisfying. Sometimes the conservatives are said to have chosen a poor leader, but in fact Iain Duncan Smith has many similarities to the pre-prime ministerial Tony Blair. He is relatively young and relatively eloquent. Journalists like him. He gives a good speech. He has a nice family. Sometimes the Conservatives are said to have "no new ideas," but that can hardly disqualify them, given that the Labor Party has no new ideas either.
The only other explanation I can come up with is connected to the scattered thoughts about the British horror of Britishness that I sent you yesterday. Duncan Smith, the sort of man who wears hats, does seem to belong to a more traditional Britain, a Britain that nobody particularly wants to associate themselves with any more. He isn't outdated, exactly, just a little old-fashioned in his looks and his manners and his biography. It doesn't seem as if he'll fit very well into the tabloid/celebrity world, in which Blair fits very well. One of the first things Blair did when he took office was to throw an immense party for all the pop stars, soap opera actresses, and other famous and half-famous people who supported him. One can't see Duncan Smith doing the same, somehow. And even though Blair wouldn't do it again either—none of those people support him anymore, anyway—he established himself as that sort of person. When Blair first campaigned for office, he threw around the word "new" so often that it became meaningless: "New Labor, New Britain, New Politics." But even if it was meaningless, people liked it, or at least responded to it. They still do, I guess.
Which means you are stuck with the "Old" National Health Service, at least for the foreseeable future. Good luck in your search for a clinic, and don't get too sick anytime soon.