I too am proud of the healthcare provided to all in the UK. The best thing by far that my government spends my taxes on. It's not without it's flaws though, but there are flaws in every system. Fundamentally this one is the most ethical and sits best with my conscience.
It does mean that you have to accept the constraints of a system, but this isn't dictated by bio-ethicists or the faceless 'big man' of government. It's done quite transparently, involving committees comprised of experts from cross sections of medical, legal, philosophical, and theological experts, as well as representatives from communities and the public.
One interesting and not so pleasant quirk of our system is that is is managed on a local/regional basis, leading to what is called a postcode (zip code) lottery. I believe it is still the case that a treatment available for a condition to one patient might not be available to their neighbour, living just yards away with the exact same condition, because their home falls under the jurisdiction of a different NHS trust who have decided on different allocation criteria. I think that there is some kind of national guidance, though non-binding, giving the trusts the ability to be flexible to the local needs and conditions in that area. But it can be a tough pill to swallow for those patients that might be denied a treatment available to others on the basis of cost. I think this is still the case.
However, I believe the greater good is delivered through this service, and it IS one of the few times that our government fundamentally do treat us all equally. The only other time I can think of in principle is in the justice system, but in reality the flaws and inequalities inherent that are even more evident.