British inflation up again, but crisis might come. What should the BoE do? According to the latest ONS report, inflation is rising as a consequence of the (pre/post) Brexit devaluation. This graph about the Input PPI is pretty revealing (taken from here):



Yet, with the risk of an oncoming economic crisis, and interest rates at record low (probably at the ZLB), what can the Central Bank do?

Some say inflation is a good thing, as it "greases the economy" by lowering real wages. But that surely will only hit the demand even more. I'm puzzled!
You could say what the chart represents.

It is in fact the changes in the input Producer Price Index http://www.ons.gov.uk/economy/inflationandpriceindices/bulletins/producerpriceinflation/july2016 with a headline statement of 


  the total input price index rose 4.3%  in the year to July 2016, compared with a fall of 0.5% in the year to June 2016


But this effect is smaller as it affects the economy as a whole.  For the output Producer Price Index the headline statement is less dramatic: 


  Factory gate prices (output prices) for goods produced by UK manufacturers rose 0.3% in the year to July 2016, compared with a fall of 0.2% in the year to June 2016.


This has not yet had a substantial effect on consumers, where for the Consumer Prices Index http://www.ons.gov.uk/economy/inflationandpriceindices/bulletins/consumerpriceinflation/july2016 the headline statement is:


  The Consumer Prices Index (CPI) rose by 0.6% in the year to July 2016, compared with a 0.5% rise in the year to June.


I would be surprised if any of today's data surprised the Bank of England:  


Imported inputs for UK producers now cost more due to a weaker Pound sterling
This has a relatively smaller effect on output prices, meaning British exporters are potentially more competitive internationally
This has not yet had a substantial impact on consumers


What the central bank does not yet know includes:


how much of an effect this will have on consumer prices in the longer term
how negative this will allow real interest rates to be if nominal interest rates are kept close to zero
how much of an effect this will have on imports and exports
how much of an effect this will have on consumption
how much of an effect this will have on investment


though it might try informed guesses.  Investment, consumption and exports in particular will be affected by broader factors including predictions about the long-term impact of a future Brexit.