Just as you allude to, Parliament has slowly gained powers from the monarch over the last 900 years. It may help you to understand which powers were won when:

13th Century - The right of the nobility to advise the King in a Great Council is enshrined in Magna Carta.

Later conflict with the nobility, led by Simon de Montford, results in the Provisions of Oxford which requires the Great Council (now called Parliament) to be called regularly and to include Knights of the Shire who serve as representatives from the counties.

Montford later calls his own, quite radical, parliament which includes non-noble representatives from towns. By the end of the century this forms the basic make up of all parliaments.

14th Century - Parliament is split into a Commons and a Lords. The most important power is gained in 1362 which requires all taxation be approved by Parliament.

Conflict with Richard II spirals in the late century. Between 1386-‘88 the ‘wonderful parliament’ showed its power by electing its own speaker, before impeaching and executing several of the Kings unpopular advisers. After a fragile period of peace Richard II was defeated by his own nobles in 1399, and Parliament voted through Articles of Deposition which stripped him of his crown and gave it to Henry IV.

15th Century - Having played an instrumental role in giving Henry IV the Crown, the Commons was able to win a series of rights from the new King. These included the right to have grievances addressed before they voted on taxation, and the right to consultation and a vote on all new laws.

16th Century - Parliament grows in power because of its use by Henry VIII to legislate on religion. It makes the King-in-Parliament the sovereign lawmaker and gives secular lords the majority in the Lords for the first time. This century also sees the first calls for Freedom of Speech in the Commons.

17th Century - In the context of Revolution and Civil War, Parliament gains control over county militias, then establishes its own army, and defeats the King. They try him for treason, which they redefine as acts against the country rather than King, and execute him.

After the restoration, conflict sprung up again between parliament and the new Stuart King. Eventually this culminated in the Glorious Revolution, where parliament invited William of Orange to overthrow James II. They vote to make William and his wife Mary joint monarchs, and vote that James II has abdicated.

Just as they did after making Henry IV king, Parliament was able to empower itself under the new arrangement. This is generally seen as the beginning of the ‘modern parliament’ and is probably the period you’re looking for.

Parliament could oversee the Kings finances, had to be elected every three years, and could refuse an oath of loyalty to the monarch.

This was the beginning of Parliamentary Sovereignty. The 17th century proved that parliament could, and would, replace monarchs at will.

18th Century - Parliament demonstrates this power by passing a law forbidding catholic’s from become monarch. It legislates to combine England, Wales and Scotland into a new nation of Great Britain through the Acts of Union. The royal veto is used for the last time ever in 1708.

When George I inherited the throne Parliament continued to empower itself. Without any real ability to speak English, or desire to interfere in British government, George I left day-to-day governance in the hands of his parliamentary ministers. Though the position wasn’t yet established, Robert Walpole is understood to be the first Prime Minister.

George II continued to act has his father had, leaving governance to his ministers and exercising power in the form of patronage of leading parliamentary figures rather than directly.

George III did not. He attempted to re-establish monarchal power but was frustrated both at home and abroad. He still ruled indirectly through loyal Parliamentary figures, but worked more closely with them than either of his predecessors.

The tipping point was defeat in the American Revolutionary War. Political opponents in parliament used the disaster as an opportunity to force the King to dismiss his favoured ministers and created an administration of those who wanted to restrict the King.

—— The changes following George III were less about restricting the power of the King and more about empowering the Commons against the Lords while extending suffrage. It’s generally accepted that the extension of the vote to poor men, and the elimination of rotten boughs, in 1832 marks the beginning of British Democracy. Though American democracy wasn’t extended to the poor until the Jacksonian period between 1828-1850.

You have to look at what happened to Parliamentary power of the centuries to decide where you want to put the marker of Sovereignty. Most historians would argue the glorious revolution marks Parliamentary Sovereignty, but argues can be made for alternative periods.

The position of Prime Minister itself didn’t come into being until the early 18th century. And it’s power varies even today because it depends upon the loyalty of Parliament.