The UK still allows private healthcare so those who really want to pay extra can do so. In several areas, for instance emergency medicine, there isn't a private offering and others the NHS has the centres of excellence available to all based on need.

While our emergency system is often at the point of creaking it at least isn't anywhere close to American levels of having to deal with what should be primary care problems. There's also the massively real hazard of what happens when you have a large proportion of the population who can't access basic healthcare, for instance a greatly increased communicable disease risk. Then there is the economic cost of people unable to work, or work as well, due to potentially treatable medical conditions or bankrupted by medical bills. On a purely economic basis there is a case for universal healthcare.