I believe I can offer the like-for-like comparison he desires. Or at least as close to one as you can get when you aren't sure how the other person came to their figure.
Inflation adjusted, around $3,000 (source can be provided on request). Lower than the vast majority of those countries provided in your chart, and without any of the associated problems that come with single payer systems (waiting lists and so on).
I might need a source so I can work out what's pushing that figure so high. The figures for 1960 NHS expenditure (inflation adjusted) seem to be way, way lower.
http://www.nhshistory.net/parlymoney.pdfPage 14, 1960/61. In today's money the expenditure on the NHS was £15bn. Divide that between the 52 million people who lived in the UK at that time and you get around £300, which is clearly a lot less than $3000 even at the roughly 3:1 exchange rate of the time. I guess that doesn't take into account private healthcare (I really can't find any source on that), but expenditure on that is very unlikely to have exceeded expenditure on the NHS, considering that even in modern times we don't spend £15bn on private healthcare per year (
closer to £10bn). So even if we're really generous and assume that somehow private healthcare had the same amount of expenditure as the NHS the UK system still seems cheaper in 1960. It's also worth noting that the sources I can find agree that the UK had a higher life expectancy than the US at the time (I'd rather a waiting list than an early death due to never having a chance to be put on a waiting list).
Looking at the table, you'll see that the cost of the NHS has gone up in spite of the government involvement not increasing. I propose that this is due to more treatments being available (thanks to scientific advances). Quite simply, we have to provide more healthcare to more people who are getting older (and thus more expensive to maintain). This is true all around the world, and I think you'll see an increase in healthcare costs in virtually any developed nation regardless of what their government did with regards to healthcare.