It is right for the Queen to consider her possible role in the Brexit showdown

The Queen’s ability to dismiss a prime minister is one of the reserve prerogative powers. These powers, which are limited, are where the Queen can still act on her own discretion.

However, it is one of the hallmarks of our constitutional monarchy that she would normally avoid exercising these powers for fear of politicising her role. This creates a contradiction at the heart of the constitution; the Head of State needs to have this power, but it is very hard to exercise. Having to make a choice over the appointment of a prime minister in controversial circumstances would be politically difficult enough; dismissing a prime minister even more so. This is why politicians are exhorted, time and again, not to drag the Queen into politics and to ensure that it is they, not her, who find a way through any deadlock.

The Palace should get advice on the constitutional questions arising from the Brexit impasse

Reports that the Palace has sought advice on the dismissal of a prime minister might seem extraordinary. But while the possibility seems remote, the reality is that the Palace needs to give it consideration – precisely because it has been raised by No.10. While the Palace will want to be clear about the circumstances in which the monarch might dismiss a PM for the first time since 1834 – when William IV dismissed Lord Melbourne – it will also want to be clear about why and when the Queen would not intervene.

Just as with prorogation, the chances of controversy are high. The Palace would want to avoid any politicised decision; its default on most prerogative decisions is to accept the advice of the incumbent prime minister. A prime minister who has no majority does not affect that default. But a prime minister who has lost a confidence vote does.

There is only one remote scenario in which the Palace would certainly intervene

If a PM lost a confidence vote, and there was clear alternative and the PM also refused to resign, then this would likely force some intervention from the Palace. It would have to listen to any clear instruction from the Commons about who they did and did not want as PM.

For now, however, the first two parts of that scenario – in which both a vote of no confidence is passed and opposition parties clearly indicate that they would support an alternative government – appear to be a long shot. Labour is refusing to countenance any caretaker PM but Jeremy Corbyn; the Lib Dems and the former Conservatives are refusing to support any caretaker PM that is Jeremy Corbyn. This might change in a moment of even greater political crisis, but it is highly unlikely that the Queen would want to intervene unless an alternative is clear.

It is unlikely that the Queen will be required to dismiss her prime minister

Boris Johnson’s No.10 have been adept at using official statements to reassure, while using anonymous briefings to create turmoil over how far it would be willing to go to get Brexit done. Despite any talk of the prime minister refusing to resign, we would have to pass through several political crunch points – the prime minister resisting to comply with the Benn Act, Labour bringing a no confidence motion, and the government then losing that vote – before we got to the extraordinary situation of the Queen contemplating the need to dismiss her prime minister.

Even if the prime minister lost a confidence vote, the Queen would probably still not become involved unless opposition parties reached an agreement on an alternative prime minister. And if an alternative is agreed, then the Queen's role is straightforward. 

No matter what No.10 may say, if this point was reached then any prime minister would almost certainly resign. If they resisted, but the Palace asked that they reconsider putting the Queen in this position, then it is even more likely that they would quit.

If they continued to resist, then the Palace may have to make clear that ‘we will have to dismiss you if you don’t step down’. This scenario really ought to be inconceivable. The fact that No.10 has implied otherwise means the Palace has had little choice but to give it proper thought.