Whether or not austerity has been successful in the UK is perhaps the most natural test of Market Monetarism. The UK, after all, has an independent central bank and there is no question as to whether or not it actually engaged in austerity (the same case can not be made for the United States, in my opinion).
It has previously been noted that, even though austerity evidently had a negative effect on real GDP in the UK, what really happened is that productivity growth just happened to be zero while Chancellor Osborne was having a fit with the exchequer. I think that the data clearly disagree with the position; as you can see both the employment rate and real GDP lagged during the period of austerity, which I will argue was only pursued fervently in 2010 and 2011, before it was significantly weakened and the economy proceeded to improve.
First, look at employment and real GDP between Q2 2010 (when the first austerity budget was suggested by the new coalition) and 2011 (the last year that the government actually maintained its commitment to austerity). It's clear that both real GDP and employment suffered during this period -- basically disproving the hypothesis that slow productivity growth and austerity were coincidental.
Of course, the government never vocally backed down on austerity, so why am I limiting my analysis to 2010 and 2011? Well, for that you need to look at the actual and the projected deficits over the course of the Cameron government:
As you can see, the actual deficit was only less than was predicted by the government during 2010 and 2011. After this, the deficit clearly begins exceeding the 2011 vintage projection; that is the government raised the deficit above what they were initially intending. It was only after this point that the economy and employment began to recover, so evidently fiscal policy was loosened in 2012 and this explains the apparent recovery that happened afterward.
The data seem to corroborate the Keynesian view a lot more than the Market Monetarist one; fiscal tightening did cause both output and employment to fall relative to trend, and the economy only began to recover with fiscal easing.