I'm not sure about the Anglo-Saxon kings, but after the Norman Conquest, yes.

William I was related to Edward the Confessor but through Edward's mother--not the usual line of succession.

Two of William's son became Kings after him: William II (Rufus) and Henry I (who married a princess descended from the Anglo-Saxon kings).

William I's grandson Stephen fought Henry I's daughter Matilda and claimed the throne, but Matilda's son Henry II inherited it from Stephen.

Henry II married Eleanor of Aquitaine and two of their sons were Kings. Richard I (Lionheart) and John.

John's son and heir was Henry III, who was father to Edward I (Longshanks).

Edward I was the father of Edward II, who was father to Edward III, who had a passel of sons.

Edward III's eldest son, the Black Prince, predeceased him, so after Edward came his grandson Richard II, who was deposed by his first cousin, Henry IV (son of Edward's third surviving son).

Henry IV's son was Henry V, and his son was Henry VI.

Henry VI was a weak king with mental illness and his reign was challenged by a distant cousin, Richard, Duke of York, who was descended from Edward III's second and fourth sons. This would be the basis of the War of the Roses.

Richard of York was killed in battle, but his eldest son took up the fight and claimed the throne as Edward IV. When he died, he was succeeded by his underage son Edward V, but the boy was deposed by his paternal uncle, Richard III, and disappeared.

Richard lost the throne and his life at the Battle of Bosworth to Henry VII, the first Tudor king. Henry was descended through his mother from Edward III through the third son, although it was considered a very weak claim. He married Edward IV's daughter Elizabeth.

Henry VII and Elizabeth had three children who factor into this. Henry VIII, Margaret, and Mary.

Henry VIII of course was father to Edward VI, Mary I, and Elizabeth I. Princess Mary's granddaughter was Jane Grey, the Nine Days Queen, who isn't always on the official list of monarchs.

Since Elizabeth I died without children of her own, the throne passed to James I (VI of Scotland), the first Stuart King. James was the son of Mary, Queen of Scots, who was in turn the granddaughter of Margaret Tudor, Henry VIII's sister.

After James came his son Charles I, who was beheaded. About 11 years after that, Charles' son came back to England: Charles II.

Charles II had no legitimate children (but a host of illegitimate ones!) so the throne went to his brother, James II.

Primarily for religious reasons, James was pushed off the throne, and his place was taken by his daughter and her husband, Mary II and William III. After they died, Mary's sister Anne ruled.

(Side note: James II had a son, best known to history as James Stuart, the Old Pretender, whose son was "Bonnie Prince Charlie." The Jacobite line.)

None of Queen Anne's children outlived her, causing a bit of a crisis. Parliament was determined to not have a Catholic monarch, which ruled out the Jacobite line. They ended going back to a daughter of James I, who had married into German royalty. This daughter had a daughter, Sophia, who married the Elector of Hanover. Sophia died a couple of months before Anne and her claim passed to her son, George.

George I and his son George II were both born in Hanover and the father, at least, was more involved in his German holdings, and we have the rise of the position of the prime minister.

George II's son died before him, so his grandson George III inherited.

George III too had a number of children, with plenty of sons. But as you may know, his health deteriorated and his mind was affected ("Mad King George"). So his eldest son became the Prince Regent (the Regency era) and later George IV.

George IV was married and had a daughter, Charlotte, but she died while giving birth and her child with her, so the throne went to George's brother William IV.

William was another with no legitimate children, so the throne went to his niece, the daughter of George III's fourth son and just barely 18, Victoria. (The Hanoverian territories went to another of George III's sons, because women couldn't inherit them)

After Victoria came her son, Edward VII, who was succeeded by his son, George V.

George V's elder son was Edward VIII, he who gave up the throne for love (later known as the Duke of Windsor); it then went to Edward's next brother: George VI, the father of the current Queen.

After Elizabeth II, the expected line of succession is Prince Charles, Prince William, Prince George, and Princess Charlotte.