I've made two previous efforts to calculate the natural interest rate for the UK, and you can find them here:

"The interest rate should be almost 3% by now" October 2015
"The neutral interest rate is currently 1.8%" June 2014

I've just written a short paper talking about why the natural rate is important, and a (very) brief summary of some recent efforts to estimate it. You download it here (data here). The charts are up through 2015, but I thought it would also be interesting to incorporate it in our data section. The chart belows shows the present situation, and as of 2016 Q2 the natural real rate was 1.8%. Using the GDP deflator as an inflation measure, this implies a nominal rate of 2.34%. With market rates (I use SONIA) at 0.47% this implies monetary policy is too loose.