Well, I usually don't turn to Slashdot for commentary, but I found one Canadian's description of Canada's health care system to be very interesting. The comments are short, so it's easy to read and the rest of this won't make as much sense unless you do.
One telling point was that the Canadian health care system might be better off if a nominal fee was charged for emergency room visits (I might extend that to all visits). A great support for this argument is Medicare. Before Medicare was first adopted in the sixties, a sizeable percentage of our elderly did not have adequate medical coverage. However, costs rose dramatically and it was eventually realized that free visits to the doctor were a lousy idea. Many elderly people were lonely and apparently took advantage of this to visit someone.
This was corrected by adding a small fee to each visit and this dramatically lowered the number of visits and made Medicare a ton of money. I don't know about how socialized medicine plans in Canada or the UK are structured, but it does seem like enacting something like that could lower useless demand quite a bit (if it's not done already, though).