Owning your own home

Between the base rate and QE that basically exactly what they have done... if you hold assets, right?

Essentially, yes. The BoE has kept interest rates very low and pumped money into the bond markets through QE in order to keep asset prices artifically high. The result has been to benefit those who hold assets at the expense of those who don't. It could be argued that the alternative would have been a massive financial crash, which would have left everyone considerably worse off (I assume that's the justification the BoW would give). Whether or not that's true, I suspect no-one knows, and I certainly don't.