From wikipedia:
'In the case of the Chagos Archipelago, in 2000, the High Court of Justice of England and Wales ruled that a local ordinance made by the Commissioner of the British Indian Ocean Territory exiling the islanders was unlawful, a decision which was accepted by the British Foreign Secretary Robin Cook. That Order was legislation passed under authority given by the royal prerogative, not an exercise of the prerogative itself, and was overturned as being beyond the powers given. After this decision, the British government issued an Order in Council, a primary exercise of the royal prerogative, to achieve the same objective. This Order was also ruled unlawful by the High Court, a ruling upheld in the Court of Appeal. However on Wednesday, 22 October 2008, the government won its appeal in the House of Lords against the previous rulings. The House decided by a three-to-two majority that the Order in Council was a lawful exercise of authority.[15][16] In their speeches, the Law Lords admitted the government of the day was morally wrong to force out some 2,000 residents of the Chagos Archipelago, a British Crown colony, to make way for a US air base in the 1960s. Nevertheless, the majority could not find legal fault in the Order.'
In actuality the privy council merely 'advises' the crown on the 'royal prerogative'.
Ultimately the crown can dissolve parliament and declare martial law.
en.wikipedia.org/wiki/Reserve_power
'
The full extent of the Sovereign's prerogatives has never been fully disclosed; however in 2004 the Government made public the following prerogatives in pursuance of trying to be more open and transparent:[citation needed]
To refuse to dissolve Parliament when requested by the Prime Minister. This was last reputedly considered in 1910, but George V later changed his mind. See Lascelles Principles.
To appoint a Prime Minister of her [his] own choosing. This was last done in Britain in 1963 when Elizabeth II appointed Sir Alec Douglas-Home as Prime Minister, on the advice of outgoing Harold Macmillan.
To dismiss a Prime Minister and his or her Government on the Monarch's own authority. This was last done in Britain in 1834 by King William IV.
To summon and prorogue parliament
To command the Armed Forces
To dismiss and appoint Ministers
To commission officers in the Armed Forces
To appoint Queen's Counsel
To issue and withdraw passports
To create corporations via Charter
To appoint Bishops and Archbishops of the Church of England
To grant honours
The power to grant Prerogative of Mercy
To refuse the Royal Assent, last exercised by Queen Anne when she withheld Royal Assent from the Scottish Militia Bill 1708.
The power to declare War and Peace
The power to deploy the Armed Forces overseas
The power to ratify and make treaties
To refuse the "Queen's [King's] Consent", where direct monarchical assent is required for a bill affecting, directly or by implication, the prerogative, hereditary revenues—including ultimus haeres, treasure trove, and bona vacantia—or the personal property or interests of the Crown to be heard in Parliament. In 1999, Queen Elizabeth II, acting on the advice of the government, refused to signify her consent to the Military Action Against Iraq (Parliamentary Approval) Bill, which sought to transfer from the monarch to Parliament the power to authorise military strikes against Iraq.
These powers could be exercised in an emergency such as a constitutional crisis (such as surrounded the People's Budget of 1909), or in wartime. They would also be very relevant in the event of a hung parliament.
For example, in the hung parliament in 1974, the serving Prime Minister Edward Heath attempted to remain in power but was unable to form a working majority. The Queen then asked Harold Wilson, leader of the Labour Party, which had the largest number of seats in the Commons but not an overall majority, to attempt to form a government. Subsequently Wilson asked that if the government were defeated on the floor of the House of Commons, the Queen would grant a dissolution, which she agreed to.[18]'