The finding that QE increased inequality is a statement of the bleeding obvious. QE has raised asset prices, and it is only the rich who have financial assets; the Bank estimates that the median household has gross financial wealth of only £1500. As Ben says, it is therefore no surprise that QE has increased inequality.
But this is not the Bank's fault. If financial wealth had been equally spread - which is a fantasy of representative agent economics more than of socialists - then everyone would have gained from QE. QE's regressive impact thus reflects the pre-existing inequality of wealth, and the Bank can't be much blamed for that*.
And the fact that the rich have benefited most from QE does not mean that others haven't benefited. People without financial assets have gained, to the (small) extent that QE has increased job security and raised inflation, thus eroding the value of debt.
There is, though, another reason to defend the Bank. In considering the impact upon inequality, what matters is the entire set of policies, not any single one.
Take a different example. Taxes such as VAT or excise duties are regressive. But we have them because they are (relatively) efficient, and we offset their regressiveness by having other progressive tax and benefit policies.
The same thing should be true of QE. If this is an effective way of supporting the economy then it should be implemented, regardless of its distributional impact. And if you don't like that distributional impact, the solution is to mitigate it through the tax and benefit system. That way, we get the benefit of QE but neutralize its unpleasant distributional effects - subject to caveats about the deadweight cost of taxes.
Rather than blame the Bank, we should blame governments - both Labour and Tory - in three ways.
1. If they had undertaken more counter-cyclical fiscal policy (which is perhaps less inegalitarian anyway than QE) there'd be less need for QE. QE is a second-best alternative (if that!) to sensible fiscal policy.
2.If wealth inequality were not so high in the first place, QE would not be so inegalitarian. In this sense, QE's adverse side-effect reflects a failure of the New Labour government.
3. The government's failure to use the tax system to neutralize QE's inegalitarianism represents a tolerance of greater inequality.
By all means, criticize the effectiveness of QE; I'll have some sympathy. But its impact upon inequality is not an argument against QE. And the Bank shouldn't be blamed for that rising inequality.
* The qualifier matters. US evidence (pdf) suggests that ordinary monetary policy has large distributional effects.