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When the wars ended, and as debt was paid off, public debt as a percentage of GDP went into a sustained decline. This happened pretty much automatically, as there wasn't much non-military public spending anyway.
This isn't the case now. The public sector is massive and insatiable.
If you actually look at the chart for the 20th Century, the debt did indeed decline steeply after the wars, and then leveled off in the mid 1970s. It remained roughly the same until 2008, when the financial crisis hit.
Secondly, your statement: "The public sector is massive and insatiable." is a non-sequitor.
The chart shows debt, not public sector spending. As I pointed out, the debt skyrocketed after the financial crisis, not because of years of public sector spending.
There are estimates of total national debt (public plus private and things like unfunded public sector pension liabilities) that approach 1000% of GDP, which puts us in 3rd place in the world behind the Republic of Ireland and Japan (just).
Which would be nonsense.
Incidentally I would be rather more exercised about the prospect of major NHS reform if the UK was coming near the top of European league tables instead of round about number 15. But of course the NHS is the "envy of the world" isn't it so it can't possibly be changed.
It comes in number 14. You should also bear in mind that:
a) Before the Nasty Party came in to power, satisfaction with the NHS was at an all-time high.
b) Pound for pound, the NHS is better value than many private systems, like the American system.
Of course the NHS can be improved, but cutting funding is not likely to produce better outcomes.
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It's also remarkable that some people complain about essential public services like health, education and pensions being 'unsustainable'. Rather, they're essential. If the state cannot provide health, education and pensions, then it is is failing as a state.
You might want to consider the fact that wealth inequality has reached such gross extremes that a small percentage of the population owns the vast majority of the wealth. Corporate taxes are being cut, and many corporations evade or avoid tax altogether. Tax avoidance and evasion together cost the treasury tens of billions of pounds per year - maybe even £100 billion.
The fact is, it's not that there isn't enough wealth in the world or the UK. We have never been richer. We have enough wealth to feed, cloth and educated every child in the UK. Instead we have a situation where the use of food banks has increased massively.
It's not because the UK is undeveloped that we're using foodbanks. It's not that we don't have enough food. Our economic system is just so insane that it has nearly ceased to function altogether. We are now mired in a decade of depression and unemployment.
Why not fight to ensure that everyone has access to the essentials in life, rather than making excuses for politicians and the wealthy to further enrich themselves?