What happened to the Glorious Revolution?

This business of the appointment of next Clerk to the House of Commons.  Here is a brief summary of the position from The Telegraph:

Mr Bercow [the Speaker] wants to appoint Carol Mills, an Australian, to be Clerk. A lot of MPs, of all parties, think that’s a mistake, suggesting she’s not qualified. This has led to an impasse. Technically, it’s up to the Speaker, as chair of the Commons Commission, to propose a new clerk. That candidate is then put forward by the Prime Minister to the Queen for approval.

I have no strong views as to the merits or suitability of Ms Mills.  What I find amazing is the involvement of the Queen.  I appreciate that it may now be a formality.  Nevertheless, why should the Queen be even marginally involved in the appointment of the most senior official in the House of Commons?  Is the House of Commons independent of the monarchy or not?  How can the Commons hold the Executive to account when the titular head of the latter has to approve appointments to the former?