Something that gives 'essentially universal coverage' - sure. But single payer, no way.
'Single payer' often means that Steve Jobs waits 12 months for his knee replacement, in behind a lot of unemployed folks, immigrants, many undocumented migrants etc. which is the objective of socialized medicine.
In Canada, it's illegal to pay a doctor to fix you. Granted, we're the only country where this is the case.
I could be wrong, but a UK friend indicated that if you 'go outside the NHS' then you have to basically stay outside of it.
The 'real challenge' is to try to find the right balance and make it fair, but still allow people to have choice etc..
Probably for 2/3rds of people, 'single payer' is best, but for a not-insignificant-minority it's definitely not.
It's tricky because I'm not sure anyone in the world has the solution.