Traditionally it has been the constitutional power of the monarch to dissolve Parliament and trigger a general election at will.
Ostensibly, the Fixed Term Parliaments Act of 2011 removed this power.
However, since Parliament derives its power from delegated royal prerogative and acts can only become law with royal assent. Is this actually binding and could the King still dissolve Parliament if he so wished, even if he had to take a few steps to repeal that law first?
Parliament derives its power from Britain's unwritten constitution, not from delegated royal prerogative. This certainly dates to at latest the Glorious Revolution. The Bill of Rights 1688 explicitly confirmed that the King has no power to dispense with laws, and the Case of Proclamations in 1610 established that the King could not legislate without the consent of Parliament. The ultimate authority in the UK is not the Queen, it's the Queen in Parliament (in other words, Parliamentary action with royal assent).
As noted in the comments, the Fixed Term Parliaments Act 2011 was repealed by the Dissolution and Calling of Parliament Act 2022. Therefore, this prerogative power has been restored.
However, as alluded to in the accepted answer, the UK Constitution is complicated. This is due to its unwritten nature. Instead, it is made up of a range of sources including constitutional statutes, constitutional case law, constitutional conventions, the royal prerogative, and authoritative legal research.
While this prerogative power exists, it is limited by the constitutional convention that the Monarch will not dissolve Parliament at will. As such the Monarch cannot, in practice, exercise this power despite having a legal right to.
The concept of these conventions can make the Constitution confusing as they are not legally binding. However, the easiest way to think about them is that they are so politically authoritative that they are treated as binding. There are exceptions, however, the conventions that limit the prerogative powers are generally extremely authoritative. This makes the possibility of this power being exercised at will effectively zero.
In summary:
Parliament is dissolved at the beginning of the 25th day before a general election under s3 of the Fixed-term Parliaments Act 2011. ss 1-2 deal with setting the dates of general elections and they are automatic, chosen (within limits) by the Prime Minister or triggered by a motion of Parliament - the Monarch has no role.
