[yrro]

This actaully happened last year. The then Prime Minister, Boris Johnson, was in a spot of political bother and it looked like the then Queen was going to sack him, as she must (according to the conventions that comprise the UK's constitution) dismiss any prime minister who cannot command the confidence of the House of Commons.

Johnson didn't want to go, so he announced (via a leak to a tame newspaper, another part of our unwritten constitution) that he would advise the Queen to dissolve parliament, in order that new elections be held. He hoped to bring rebellious Tory MPs in line by threatening those in marginal seats with defeat, and those in secure seats with the prospect of a lengthy spell in opposition.

The Palace put paid to this plan by informing the PM that the Queen would be unavailable to meet with him, in the event of him perhaps wanting to to her in order to dissolve parliament.

And the rest is history!