That is true, but it merely means that the Bank of England is not totally independent of political control. And if we have an independent European Central Bank the degree of political control by the British, at least, will be very low indeed. Central Banks are intrinsically conservative These days appropriate monetary policy basically means appropriate interest rate policy. Appropriate interest rate policy depends on a number of things. There are always some people changing jobs or retraining.
Some unemployment is entirely natural.
If current unemployment is above the NRU then that is a source of deflationary pressure. The extra unemployed people will be looking for jobs and thus bidding down wages, hence production costs, and hence prices. Roughly speaking, the higher deflationary pressures are, the lower interest rates will be. In contrast, if unemployment is below the NRU that is a source of inflationary pressure. There are not enough people switching between jobs, and there is not enough retraining going on, so workers are scarce.