Not quite ... the Governor General acts on authority derived from the Crown, and used that authority himself to dismiss the Australian PM. So it wasn’t the Queen wot did it, even though historic crown powers were used.
Queen can sack the Governor General, but ironically she would only ever do so on advice from her Australian PM. So really the PM should’ve moved first.
In the U.K. the Queen is the one who appoints PMs and has the power to dismiss them, and also to dissolve Parliament, but she only does so on advice.
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You are legally incorrect, and based on the contents of the very thorough public debate prior to the vote you are not correct in the spirit of the law either.
The referendum was advisory because it only ever can be so in our constitution. Its mandate lies only in the precedent that what is voted for, is done. This was established in the first referendum ever held in the U.K., on our EU membership in 1974, in three devolution referendums, a Westminster election voting system referendum and one on Scottish independence.
Of these, only the Welsh and Scottish devolution referendums of 1998 have changed the status quo; in both cases, the way in which the referendum result was implemented was by consultation, forming government policy, and finally by whipped votes in Parliament. Ultimately the devolution bills presented by Blair’s government were passed. The nationalists continued to blow hard over it but that’s what happened then, and it’s what needs to happen now. Government policy must be implemented as stated in the manifestos we voted on in 2016.
And the Commons fully realises nothing - it is split as never before, because when push comes to shove MPs know that the power to legislate is theirs, not ours; because both main party leaders are the weakest in living memory; because we have now had a hung parliament for 7 of the last 9 years and the Commons has become a place where horse trading and personal preferences have begun to take precedence over the party manifestos MPs pledge to support in return for the major advantage of running as an official candidate.