Kings & Queens of England
Those descended from English monarchs only through an illegitimate child would normally have no claim on the throne, but the situation was complicated when Gaunt & Swynford eventually married in 1396 (25 years after John Beaufort's birth). In view of the marriage, the church retroactively declared the Beauforts legitimate via a papal bull the same year, & Parliament did the same in an Act in 1397. A subsequent proclamation by John of Gaunt's legitimate son, King Henry IV, also recognised the Beauforts' legitimacy, but declared them ineligible ever to inherit the throne.
Nevertheless, the Beauforts remained closely allied with Gaunt's other descendants, the Royal House of Lancaster. John Beaufort's granddaughter Lady Margaret Beaufort was married to Edmund Tudor. Tudor was the son of Welsh courtier Owain Tudur (anglicised to Owen Tudor) & Catherine of Valois, the widow of the Lancastrian King Henry V. Edmund Tudor & his siblings were either illegitimate, or the product of a secret marriage, & owed their fortunes to the goodwill of their legitimate half-brother King Henry VI. When the House of Lancaster fell from power, the Tudors followed.
By the late 15th century, the Tudors were the last hope for the Lancaster supporters. Edmund Tudor's son became king as Henry VII after defeating Richard III at the Battle of Bosworth Field in 1485, winning the Wars of the Roses. King Henry married Elizabeth of York, daughter of Edward IV, thereby uniting the Lancastrian & York lineages.
With Henry VIII's break from the Roman Catholic Church, the monarch became the Supreme Head of the Church of England & of the Church of Ireland. Elizabeth I's title became the Supreme Governor of the Church of England.
The House of Tudor 1485-1603
Edward VI named Lady Jane Grey as his heir in his will, overruling the order of succession laid down by Parliament in the Third Succession Act. Four days after his death on 6 July 1553, Jane was proclaimed queen the first of three Tudor women to be proclaimed queen regnant. Nine days after the proclamation, on 19 July, the Privy Council switched allegiance & proclaimed Edward VI's Catholic half-sister Mary queen. Jane was executed for treason in 1554, aged 16.
Following the death of Elizabeth I in 1603 without issue, her first cousin twice removed, King James VI of Scotland, succeeded to the English throne as James I in the Union of the Crowns.
James was descended from the Tudors through his great-grandmother, Margaret Tudor, the eldest daughter of Henry VII & wife of James IV of Scotland. In 1604, he adopted the title King of Great Britain. However, the two parliaments remained separate until the Acts of Union 1707.
House of Stuart 1603-1649
No monarch reigned between the execution of Charles I in 1649 & the Restoration of Charles II in 1660. Between 1649 &1653, there was no single English head of state, as England was ruled directly by the Rump Parliament with the English Council of State acting as executive power during a period known as the Commonwealth of England.
In 1653, Oliver Cromwell forcibly took control of England from Parliament. He dissolved the Rump Parliament at the head of a military force & England entered a period known as The Protectorate, under the direct control of a single individual known as the Lord Protector.
While not officially monarchs, the holder of the office of Lord Protector passed from Oliver Cromwell to his son Richard. Richard lacked both the ability to rule & confidence of the Army, & he was forcibly removed by the English Committee of Safety under the leadership of Charles Fleetwood in May 1659. England again lacked any single head of state during several months of conflict between Fleetwood's party & that of George Monck.
Monck took control of the country in December 1659, & after almost a year of anarchy, the monarchy was formally restored when Charles II returned from France to accept the throne of England following the Declaration of Breda & an invitation to reclaim the throne from the Convention Parliament of 1660.
House of Stuart (restored) - 1660 - 1707
After the Monarchy was restored, England came under the rule of Charles II, whose reign was relatively peaceful domestically, given the tumultuous time of the Interregnum years. Tensions still existed between Catholics & Protestants, however, & with the ascension of Charles's brother, the openly Catholic James II, England was again sent into a period of political turmoil. James II was ousted by Parliament less than three years after ascending to the throne, replaced by his daughter Mary II & her husband (also his nephew) William III during the Glorious Revolution. While James & his descendants would continue to claim the throne, all Catholics (such as James & his son Charles) were barred from the throne by the Act of Settlement 1701, enacted by Anne, another of James's Protestant daughters.