That would be William of Orange, who deposed James II at the invitation of England's Protestant lords. At first they wanted to make his wife, Mary, sole ruler, but William insisted (backed by Mary) on being fully vested as king in his own right. After Mary's death, William ruled as sole monarch for eight more years.

William and Mary had no children, so Mary's sister Anne took the throne. Anne also had no children. In 1701, Parliament passed the Act of Sucession. This barred Roman Catholics from the line of succession - as a result, the closest Protestant relative, Duke George of Brunswick-Lüneburg, leapfrogged fifty closer Stuart relatives to become King George I of the House of Hanover when Anne died in 1708.

Simplified version:

Henry the VII of England defeated Richard III in the Battle of Bosworth Field to end the War of the Roses.

• Henry's Son was Henry VIII who became king
• Henry VIII's Son Edward VI became king after Henry
• Mary I, Edward's Half Sister, became queen after Edward Died
• Elizabeth I Edward and Mary's half sister (Henry VIII had multiple wives if you recall the song) Became queen after Mary died
• James I (Henry VII's great-great-grandson) became king when Elizabeth I died childless
• Charles I, son of James I, became king after James died
• ! Oliver Cromwell had King Charles executed, and became protectorate after winning the English Civil war. There was no king during this time
• Charles II, Son of Charles I was invited back to be King after Oliver Cromwell died
• James II, Son of Charles II, became king after Charles II died
• William III, Grandson of Charles I, became king after James II got kicked out. William was invited to be king by members of the government of England and became king [mostly] without bloodshed. This was known as the Glorious Revolution.
• Anne, Daughter of James II, became queen when William III died
• George I, great grandson of James I, Became King when Anne died, due to the act of settlement which prevent Roman Catholics from becoming Monarch. George was the closest protestant relative of Anne
• George II, son of George I, became king when George I died
• George III, grandson of George II, became king when George II died
• George IV, son of George III, became king when George III died
• William IV, son of George IV, became king when George IV died
• Victoria, granddaughter of George III, when William IV died with no legitimate children
• Edward VII, son of Victoria, became king when Victoria died
• George V, son of Edward VII, became king when Edward VII died
• Edward VIII, son of George V, became king when George V died
• George VI, the younger son of George V, became king when Edward VIII advocated to go marry an American Woman
• Elizabeth II, daughter of George VI, became queen when George VI died

So that brings us to now.

So the line goes [Bracketed names were never English monarchs]:

0. Elizabeth II ->

1. George VI ->

2. George V ->

3. Edward VII ->

4. Victoria ->

5. [Prince Edward] ->

6. George III ->

7. [Fredrick Prince of Wales]

8. George II ->

9. George I ->

10. [Sophia of Hanover] ->

11. [Elizabeth Stuart] ->

12. James I ->

13. [Mary Queen of Scots] ->

14 ) [James V of Scotland] ->

15. [Margaret Tudor, Queen of Scotland] ->

16. Henry VII

So my count is 16 generations removed, between both the male and female line, which danced in and out of the English monarchy, since an English King took the throne by force.

Edit: Oops, made some mistakes.