The National Health Service is, or at least was, a near monopoly. Monopolies are a bad thing and therefore we want to break up the monopoly.

However, there's long been a school of thought that says that monopolies, while they might not be positively good things, aren't actually all that bad. It might be acceptable to have the teensie, tiny, costs of monopoly if there is some over-arching reason to do so. Like, for example, the much vaunted "fairness" of equally bad access to healthcare for all. This argument rests on the costs of monopoly being teensie. They ain't [3]:

This paper reports on a new literature that takes a different approach to the costs of monopoly. It examines the costs of monopoly and tariffs within industries. In particular, it examines the histories of industries in which a monopoly is destroyed (or tariffs greatly reduced) and the industry transitions quickly from monopoly to competition. If there are costs of monopoly and high tariffs within industries, it should be possible to see those costs whittled away as the monopoly is destroyed. In contrast to the prevailing consensus, this new research has identified significant costs of monopoly. Monopoly (and high tariffs) is shown to significantly lower productivity within establishments. It also leads to missallocation within industries: Resources are transferred from high- to low-productivity establishments.

Thus we want to break up the monopoly. Indeed, we've seen evidence of rising productivity as a result of the limited competition already extant. Two data points: NHS England had limited competition between establishments while NHS Scotland and Wales did not. Productivity (ie, amount of treatment, number of treatments and quality of treatments for the same money) rose in NHS England in a way that they did not in Wales or Scotland. Secondly, we found that when limited competition (on quality not price grounds) was introduced in NHS England that those areas with more competition increased productivity (same measure, more and better treatment for same cost) more than those areas with less.

New theory tells us that monopoly is worse for productivity than we had thought. If this were so then relaxing the monopoly should result in an increase in productivity. We have so relaxed and we are seeing increases in productivity. Thus we desire to relax the monopoly.

None of this stops the tax financing of at least some health care of course. It is only an argument about the mechanism by which the actual service is delivered: not by a monopoly please.