I am a student of molecular biology, I have studied cancer and I'm about to take a course specifically in cancer biology. I have had 2 close family members survive cancer, and
one of them survived due to very new and top line medical treatments. Cancer absolutely indicates the quality of a countries health care system, because it takes the newest research, machines, and therapies in order to reach a survival rate that high. It's also due to the quality of medical testing. The article I cited said one reason why the UK ranks so low is because of the waits in their healthcare system. People make an appointment and get to the doctor too late, and so the cancer is harder to treat. I searched for other statistics and I couldn't find anything beyond cancer. However, I did find this chart which depicts deaths related to heart disease.
Heart disease deaths statistics - countries compared - NationMaster
7 United Kingdom: 122 per 100,000 people
13 United States: 106.5 per 100,000 people
Honestly I was shocked by this considering America has a higher obesity rate (and epidemic) compared to the UK. I think it can be inferred from the data presented that one main reason why the US heart disease related deaths is lower could be due to our superior quality of care.