That's something of a problem, that economic history is not actually as a lot of economists think it is. Here, for example, is Paul Krugman on the current UK recovery:
Britain’s economic performance since the financial crisis struck has been startlingly bad. A tentative recovery began in 2009, but it stalled in 2010. Although growth resumed in 2013, real income per capita is only now reaching its level on the eve of the crisis — which means that Britain has had a much worse track record since 2007 than it had during the Great Depression.
The rest of the column is about austerity, wrong economic policy, Keynes, you get the general picture. However, Britain's economic history in the 1930s is really not what is being assumed there. In fact, it's Britain's economic history in the 1930s which gave us the whole idea of expansionary austerity....which actually showed it could work.
What Neville Chamberlain did was to take Britain off the gold standard and allow the corrency to devalue (about 25%). At the same time he cut government spending significantly and brought the budget back into some kind of balance. This actually worked: By 1934 Britain was back above 1931 levels of output and it all became just a nasty blip unlike that Depression that the US suffered (the 1920s in te UK were a different matter). That is, fiscal austerity combined with monetary laxness worked and worked very well.
Krugman wants to tell us that it hasn't worked this time: OK, that's fine, it hasn't worked in hte same manner. Krugman also wants to tell us that fiscal expansion would have: but that's to miss the lesson of the 30s. Osborne devalued the pound and had that loose monetary policy through QE. This should have worked as before: but it didn't. What was the one thing that Osborne didn't have? Fsical austerity. So, expansionary austerity worked once, didn't work a second time. And what wsa different was that the second time we didn't actually have the austerity. This isn't an argument that therefore expansion would have worked: it's simply a note that we didn't actually do what worked last time.
Please note, we're not actually arguing that repeating Chamberlain's actions would have worked this time. Rather, we're remarking upon the misunderstanding of what he did, that misunderstanding of what history was. The UK's 1930's recovery is proof that that basic idea, of expansionary austerity, can in certain circumstances work. We cannot therefore go around using it as an example of it not working. and if we do want to apply that lesson to today then the answer would be that it's not worked as well this time around because there hasn't actually been any austerity, even if the monetary policy has been spot on.