Does Michael Saunders of the Bank of England think QE doesn’t increase inequalities?

It rather looks like it according to an FT article entitled “BoE must be ‘constantly on alert’”. Let’s run thru this very slowly.
 
QE consists of the central bank printing money and buying assets, mainly government debt. Now if a new buyer with a very deep pocket enters a market, prices of items on sale in that market have a tendency to rise. Or have I missed something?

And assets (houses, shares, government debt, you name it) tends to be held by the rich: not those living on social security. Ergo QE increases inequality. Or have I missed something?

Indeed, the BoE’s own research supports the idea that QE increases inequality.
 
Not that I object to that inequality effect too much because when we’ve QEd the ENTIRE national debt, we’ll then be in what Milton Friedman and Warren Mosler considered the optimum position: having no government borrowing at all.

This is a classic case of “Pareto optimality trumps everything else”. That is, if a change raises GDP (which it does according to Friedman and Mosler), then any increased inequality can be countered by redistributing money from winners to losers. Net result: everyone is better off, or at least they can be, depending on exactly how the redistribution is done.