One reason for the inflation figure not moving after QE might be that there is something missing from the inflation measure used. So we look a little closer and, lo and behold, it doesn't include property prices ( apart from "imputed rents" which is a fabricated value with no connection to reality ).
Essentially QE has inflated asset prices, essentially transferring wealth from the majority to the minority, while exposing the BoE to potentially huge losses when it eventually has to unwind its position (which liability will,of course, be covered by the taxpayer). In addition, one effect of QE pushing up bond prices and hence forcing down interest rates is to force companies with final salary pension schemes* to put additional money into those schemes that would otherwise have been available for investment - one estimate I saw was this effect would total about 70 billion pounds.
* ( although these schemes are now rare outside of the BoE, there are plenty that were closed to new employees years ago but will have ongoing liabilities for many years yet )
Oh, and the recent 0.25% rate cut comes after the fall in Sterling which, according to the BoE's own "rule of thumb" will have an effect roughly equivalent to a rate cut of 2.0% .