However, it's not taking your freedom away -- it's trading one kind of freedom for another: the freedom to not pay for collective welfare for the freedom from your (or your dependent's) health being used coercively during labor negotiations or to extract rents.
On balance, I think that the freedom to have less social responsibility is less useful than the freedom to be healthy regardless of employment status or job transitions, particularly since it saves me money.
I have more money to spend (because of less rent extraction from healthcare) and am freer to pursue my economic goals (because I am less dependent on an employer for my health).
To me, it simply sounds like I'm freer by having socialized medicine.
But since no one wants either, the pressure usually ends up on doctors. If there is an exodus from the public sector, instead of a slow downgrade, then it will collapse.
edit: the original point is that the US should have a system like the UK - but is the NHS even sustainable?
The problem of rising healthcare costs is a real one, not an artefact of a particular system, and there is no easy fix for it.