The problem is WHERE do the 40% of Brits that aren't satisfied with their "FREE" system go for recourse and HOW could only 61% of folks be satisfied with a "FREE" service. Hint: The 60% that are satisfied are folks that have never had to use the system except for minor ailments.
Single payer is ABSOLUTELY great for giving vaccinations and passing out antibiotics. However, since "FREE" services tend to become very overused, very quickly, in order to keep the system from spending every dollar or lb from here to eternity, services MUST be rationed. I can sue my ins company if they won't pay for a needed service or if they won't allow me to be treated in a timely fashion. If a private insurer only contracts with enough doctors to provide a hip replacement after an 18 mth wait, they will be out of business shortly. A government system that fails to perform efficiently just grabs more money until there is no more money then the inevitable shortages and rationing arrives.
You see, until O'care, if I thought my insurers weren't living up to their promises and I had recourse available to me. I could switch plans. Under O'care, I still have a right to sue if my insurance company doesn't deliver needed services but that right will be limited as costs begin to explode and insurers begin to seek relief to stay viable. Under a fully operational single payer system where the government takes over, you no longer have recourse and since government employees don't care if the government gets sued, you will see quality of care suffer.