London (CNN) The United Kingdom, once a beacon of political and diplomatic stability, has descended into chaos since it voted to leave the European Union in 2016.

That referendum opened a seemingly unbridgeable divide that has led to political deadlock and stretched Britain's famously unwritten constitution to its limits.

The Supreme Court will try to pick a way forward this week, but ultimately, it could come down to Queen Elizabeth II to pick side. And that's something the Queen will be desperate to avoid.

The court case hinges on whether Prime Minister Boris Johnson misled the monarch when he advised her to suspend, or prorogue, Parliament

Johnson said the prorogation was necessary to start a new parliamentary session and to give time for the political parties' annual conferences. But Scotland's highest court declared last week that the real reason was to stymie Parliament by cutting back on the time available to debate Brexit options.

"And indeed as I say, the High Court in England plainly agrees with us," he said, referring to an earlier judgment in a separate case made by judges in London. The only problem was that the English court didn't agree with him. It merely said it didn't have the power to rule in the case, which is why it too has been referred up to the Supreme Court.

Eleven justices will hear both cases this week. Their judgment will be binding.

The Queen invites Boris Johnson to become Prime Minister at Buckingham Palace on July 24.

Historians are yet to find an example of any Prime Minister being found guilty of misleading a monarch.

"The government must obey the law," said Vernon Bogdanor, research professor at King's College London and the author of "Beyond Brexit: Towards a British Constitution."

"If the law is that Parliament cannot be prorogued, then it must be recalled, and the advice to the Queen rescinded. If the PM breaks the law, then he will be prosecuted and brought before the courts just like any other citizen," Bogdanor explained.

A ruling against the government would leave Johnson with the unpalatable choice of being hauled up before a judge or going back to the Queen and asking her to overturn his previous advice.

Embarrassing for the Prime Minister, it would be uncomfortable for the Queen too. The monarch does everything she can to avoid the political process beyond her ceremonial duties.

Unlike her counterparts in other constitutional monarchies like Denmark and Belgium, she doesn't even see a role for herself in mediating between political parties when they reach an impasse.

Bogdanor believes the outcome of the case will likely hinge on the length of the prorogation.

"The court would probably not rule that there should be no prorogation at all, since the parliamentary session has already lasted for two years, a long time by our standards," he said, adding that the court might say the suspension "should be much shorter."

"It is reasonable and normal for a government in these circumstances to seek a new session after a short prorogation of a few days," he said.

The Queen retains her political independence by sticking rigidly to the long-established convention of only ever acting on the advice of the Prime Minister. So, when she was asked to approve the suspension of Parliament, she did so without questioning it.

But if she wasn't given a full explanation for the suspension then the court could rule she was misled.

She probably wouldn't divulge her personal feelings, but such a ruling would hardly set a positive tone for Johnson's weekly audiences with the Queen -- a tradition his predecessors valued highly.

The Queen is a font of knowledge, having counseled every PM since Winston Churchill.

For the Queen, the worst-case scenario would be to be placed in a situation where she would need to make a political decision.

Winston Churchill kisses Queen Elizabeth II's (R) hand as she leaves 10 Downing Street in 1955.

But what if the Supreme Court rules against Johnson's government and orders him to recall Parliament, but he refuses to do so immediately?

There would be public uproar, and all eyes would turn to the Palace.

Does the Queen sit and wait for Johnson, or go against convention and act on the court's judgment?

Her options would be the subject of intense public debate which would go to the core of why and how the monarchy even exists.

It would also set a precedent for her successors. At the back of her mind would be her core duty to leave the Crown in a stronger position than when it was passed to her. The public response to this potential constitutional crisis would also weigh heavily on her.

The Queen has been tested before in her long reign and she came out stronger. But she is surely hoping not to be tested again by this week's case.