Before 2008, an avowedly modernising Conservative party committed to match Labour's public spending totals. However, two weeks after Lehman Brothers went bust in 2008, George Osborne took to the rostrum at his party's conference and reverted to Tory type, sternly announcing that "borrowing is out of control", and – recalling an establishment phrase from the Depression – promising to "put sound money first". There is something ironic in this ancient echo, for – as we will show – the Osbornian claim that Britain is broke is dependent on eschewing the long view.

By the time the coalition was created, the early stirrings of a debt crisis in southern Europe lent superficial credibility to fears that Britain was teetering on bankruptcy. And so the cutting began, with the squeeze disproportionately concentrated on capital outlays, such as building projects. In just two years, net public investment almost halved from £48.5bn in 2009/10 to £28bn in 2011/12, and despite recent budget hype about renewing the infrastructure, the smallprint of the red book reveals that this net investment total will stay on the floor, averaging only £25.8bn per year during the first half of the next parliament.

The defining narrative remains that There Is No Alternative, because Britain is "broke". But can this story be squared with the facts?

The figure below shows that UK debt/GDP was above 80% for most of the last 300 years. Enthusiasts for austerity tend to ignore the vast majority of that timeframe, focusing on the increase in debt from below 40% to around 80% of GDP in the last few years. But If Britain is broke at the moment, then the graph shows that it was also broke for a whole century between 1750 and 1850, and for 20 years after the second world war. In reality, in neither case did the UK default, and reveal itself as bust – both periods were times of investment, growth and national renewal.

Graphic - UK GDP since 1692

Other advocates of austerity suggest Britain is broke because the cost of servicing debt is bankrupting us. However, UK debt interest payments are now actually lower as a share of GDP than at any point up to the year 2000. So if this is the yardstick for being "broke", Britain has also been broke over the whole second half of the 20th century.

Of course, modest current costs would be of no comfort if they were liable to rocket soon. The reality, however, is that there is no sign at all of increased public debt pushing up public borrowing costs. Since the slump first swelled the debt in 2008, interest rates have drifted not up, but downwards. Most chancellors in the late 20th century would have given their right arm to be able to borrow at anything like the current 2%.

Furthermore, research by Jonathan Portes, of the National Institute of Economic and Social Research (NIESR) suggests that rates fell to such lows during this slump because the prospects for growth are so weak – not because austerity has persuaded investors that the UK is less likely to default.

All evidence, then, points against Britain being too bust to invest. But shouldn't the UK still fear going the way of Greece – losing control of the public finances – and then, after a delay, being savagely punished by the markets?

Not really: the problems of Greece and other stricken continental economies arise because they have no flexibility to unilaterally loosen their monetary policy, owing to euro membership. In contrast, with its own central bank the UK enjoys more freedom to grow its way out of recession. Indeed – while inflation remains depressed – if the UK were in a tight corner it could simply print the funds required to avoid outright default.

Britain, then, is not "broke" – in any historical terms, it is ludicrous to claim that. As for Britain not being able to afford to invest, the truth is the exact opposite: with the cost of borrowing at historic lows, Britain cannot afford not to invest. As in the 1930s, George Osborne's "sound money" philosophy is distinctly unsound economics.

• This mythbuster is part of a series co-ordinated by the New Economics Foundation and the Tax Justice Network. You can read the full length piece here