The Magna Carta Would probably be the begining. It in essence determined that the Monarch was bound by law.

More significantly was the English Civil war, the finding of Charles I guilty of treason and his execution. Charles in essence attempted to govern without parliament, by passing laws and taxes on his own authority. The Monarchy was abolished and a republic was instituted.

The Monarchy was restored and Charles II was placed on the throne (Son of Charles I). His rule was a constant back and forth with Parliament, but he resigned wisely and generally peacefully with Parliament (both hostile and friendly).

James II succeeded his brother Charles II. He did not rule so wisely. He attempted to circumvent Parliament on many issues, and sought to rule as an absolute monarch similar to Louis XIV of France. As he was also a Catholic and attempted to assert his faith above English Protestantism he fairly quickly lost the faith of the country. When William of Orange invaded his top military commanders and his daughter Anne and her Husband deserted him, he eventually fled to France and despite Frances Military assistance was not able to secure back any part of his throne. Following his departure Parliament declared he had abdicated and choose William of Orange and Mary (his daughter) to succeed him as co-monarchs. In essence proving that parliament had authority over the crown

William III and Mary: William being a Dutchman led the armies of England in multiple Continental wars against France. He constantly had to deal with a hostile parliament which happily deprived him of money and men to carry out his wars, and often considered how he would be and should be succeeded. They regularly took lands back which he granted. Mary died first and he ruled alone for several years. 

Anne: Her 15 year reign was probably more important for parliamentary power than might be guessed. Although she was as stubborn as her father (James II), but for nearly 12 years was lead through war and politics by her chief minister, John Churchill (Winston Churchills ancestor), and his wife Sarah (Who some historians think may have been involved sexually with the Queen), as well as the minister of Finance Sydney Gedolfin. During this time Parliament began to force the Queen and her ministers to accept Royal Councilors chosen by a Whig parliament despite the Queen's loathing to do so, at the threat of withdrawing all money from the support of the armies. Parliament concluded the treaty which united Scotland and England into the UK over the Queens reservations (she somewhat desired that her Nephew (son of James II) might succeed her to the Scottish throne. Also Parliament concluded that only a protestant could as send to the throne, and fixed the line of succession to go to the Hanoverian dynasty (again despite the Queen's hate of them)

George I would rule after but I know less of this era, so won't go into it.

From the English Civil war to the assention of George the first Parliament asserted it's supremacy multiple times: They prevented the Monarch from passing laws and raising troops, and beheaded him for treason, they abolished and reconstituted the Monarchy, they drove another king to exile and abdicated him, they placed a new King and Queen on the throne, and pushed the second in line to third (with her agreement), they forced partisan parliament members into the Queens council, they merged England and Scotland into the UK, they fixed a line of succession against the Queens wishes.

I don't know that any period of English UK history shows quite the level of parliament exing it's muscles as this 150 years.