Brad DeLong thinks I'm nutty when I say that Britain isn't obviously suffering from a persistent shortfall of aggregate demand:

There are no signs looking at wages and prices that this is due to any adverse supply shock...there seem to be no reasons looking at wages, prices, and output to believe that the British economy right now is a full-employment at-capacity-utilization economy. And only in such an economy would monetary and fiscal policies that boost spending simply boost prices and not production...

Does the fact that the employment share of British adults is actually high mean that the British economy is, in fact, at potential output? That stimulative monetary and fiscal policies risk rising inflation for no gain? And that it is time to normalize? Certainly Mark Carney at the Bank of England does not believe that is so:

From my point of view, why so many Britons have taken so many low-pay low-productivity jobs in the past three years is a mystery. But that they have gives us little reason to think that the British economy is now a full-employment at-capacity-utilization economy in which aggregate demand is now equal to potential output.

First of all, let's get a couple things straight. I don't think British stimulus would be particularly counterproductive, I just don't think austerity would be either. If there's not a big demand gap, multipliers shouldn't be large, so stimulus just won't do a heck of a lot (unless the UK has falling-apart infrastructure like we do), but neither will austerity. Also I doubt AS-AD is even always the right model for the macroeconomy.

But with that said...

With a demand shortfall, we ought to see high unemployment. We also ought to see low inflation.

In the U.S. we saw both of these in 2009-2014. In Britain we saw the former in 2009-11, and we never really saw the latter at all. Here is British core inflation:

The Bank of England's inflation target is 2% (whether that's a ceiling or a target is not certain). But in 2010-2013 - four years!! - UK core inflation was above that target. 
So if we stick to the good old Econ 102 AS-AD model, and we look at both prices and quantities, we can come up with the following simple story for the UK:
1. In late 2008 the UK suffered a negative AD shock.
2. Around the same time, the UK suffered a negative AS shock.
3. In early 2010 the negative AD shock began to abate.
4. In 2012 the negative supply shock began to abate.
5. The differences between the UK and the U.S. in GDP, employment, and inflation can be explained by the fact that the UK's AD shock wasn't quite as big or long-lasting, while the U.S. didn't experience a supply shock.
This story also fits what we know about British TFP, which declined from 2007-2009, then flatlined through 2011:

This story is incredibly simplified, and uses a model that probably isn't the best. A real, careful, academic analysis of the situation is certainly warranted. But is there some obvious reason we need to go looking for a story where AD is the only thing moving around here? That story is going to have a lot more moving parts, and it's going to go a lot deeper into micro stuff. 
And it will also look like reaching. Why should we demand a story where demand is the whole story? Is this about stabilization policy, or about the size of the British state?