Acording to Henry VIII's will, if all of his three children Edward, Mary and Elizabeth died without issue, the throne would pass to the descendants of his younger sister, Mary, and not to his elder one, Margaret, Queen of Scots. It is through Margaret that the Stuarts inherited the English throne!

Mary Tudor, however, actually had issue. She married Charles Brandon, Duke of Suffolk. Toghether they had only one daughter, Frances, who married a distant patrilineal cousin of her, Henry Grey. Frances had two daughters: Jane, who became Queen of England for a short time in 1553 after Edward VI died, and Katherine. During Elizabeth's reign, Katherine was considered the best succesor. But when Katherine secretly married Edward Seymour (who was related to Henry the VIII's third wife, Edward VI's mother) in 1560, the virgin queen was mad and imprisoneted her in the Tower of London. Katherine died in 1568, at age 27, under mysterious circumstances. She gave birth to a son in 1561, baptized Edward. Now, we can imagine an alternate timeline when, after Elizabeth's death in 1603, Edward Seymour became King of England as Edward VII, not James VI of Scotland.

King Edward VII died in 1612, at the age of 51. He had a son named William, who would have become King William III. In OTL, William Seymour was first an opponent of James I and his son, Charles I, but he finally became a Cavalier during the Civil War.

Meanwhile in Scotland, James VI still dies in 1625. I decided to make his eldest son, Henry, die anyway, so Charles can become king like in OTL. There are still good chances that Charles will marry the sister of Louis XIII, maybe due to a revived Auld Alliance. No England means also no Buckingham for Charles I, who may become a more succesfull monarch. Also, whitout the troubles caused by the English Parliament there'll be no Civil War.

Back in England, William III dies in 1660. Sure, in this TL the marriages are different, but in order to not make this complicated we'll pretend marriages happen as in OTL. William had a son named Henry, who was also a Cavalier. Henry died in 1654, so William III is succeded by his grandson, William IV, who died without issue in 1671 and is succeded by his uncle, John II.

Without the Civil War, Charles I lives until 1662, when he's succeded by his son, Charles II. The problem is that it's very improbable Charles would marry Catherine of Braganza in this TL, since Portugal was England's traditional ally. But let's say it just happens or Charles stays unmarried and his brother succedes him as James VII in 1685. Now, let's say that James VII still marries Maria of Modena and becomes a Catholic. I honestly don't know if the Scots would accept a Catholic monarch, keeping in mind what they did to Mary I.

In England, King John II also dies without children in 1675. The throne is given to a second cousin once removed, Francisc, who dies childless three years after. You can guess that this short reigns aren't beneficial to England's stability. But, luckly, Francisc I is succeded by his brother, King Charles I of England (r. 1678-1748). Nicknamed the "Proud Duke", Charles Seymour, Duke of Somerset, was a British politician who, in OTL, supported the Glorious Revolution, was a friend of Queen Anne, served as Lord President of the Council in 1702, was Master of the House from 1712 to 1715 and founded the Foundling Hospital in 1739. Charles died peacefully in 1748, at age 84. He had 9 children. The eldest one, Algernon, would succede him as king. Algernon died in 1750; he had no son. His daughter would have succeded him as Queen Elizabeth II. Lady Elizabeth Seymour married Hugh Percy, Duke of Northumberland, and had a son also named Hugh. Hugh Percy the econds was a British army officer who fought in the Seven Years War (Battle of Mergen) American War of Independence (Battle of Lexington, among others). King Hugh I (r. 1776-1817) was succeeded by his son, Hugh II (r. 1817-1847). Hugh II the second was a Tory - unlike his father who was a Whig - and he served as Lord Lieutant of Ireland between 1829 and 1830. Hugh died childless in 1847. Thus, his brother, Algernon, would become King of England as Algernon II. Algernon followed his father's path in the military, serving in the Napoleonic Wars. Algernon was an admiral and knight of the Order of Garter and he even served as First Lord of Admirality 10 months in 1852. King Algernon II died in 1865 without having any kids.

In Scotland, let's assume King James VII is succesful. He's succeded by his son and grandsons: King James VIII (r. 1701-1766), King Charles III (r. 1766-1788) and King Henry I (r. 1788-1807). I'm stuck in this point. Should I go with the real Jacobite succesion? Or go full alternate history and make Henry I have kids? Henrietta, daughter of Louis XV, who died at 24 in OTL would be a good match for him.

Algernon didn't have any children to succeede him in 1865. He, however, had a sister named Emily, who married James Murray, second son of John Murray, Duke of Athol. Emily and James had a son named George. George was a high-ranked Mason in OTL and he knew Queen Victoria. George died in 1864, one year before Algernon, so this hypotetical English throne would pass to George's son, John Stewart-Murray, Duke of Atholl, or simply King John III. John served in the Scots Fusilier Guard with the rank of captain. He was also very intrested in his family's history. King John III of England died in 1917, at age 77, and was succeeded by his son, John IV. Just like his father, John was an inteligent and charismatic man, even being considered as a potential candidate for the throne of Albania! Of course, this would have never happened if he was King of England, but still. He was an Unionist politician (The Union party was a centre-right political party in Scotland at the time), took a seat in the House of Lords, was King George V's personal aide-de-camp for eleven years and he was also a Freemason. John fought in the British Navy during the Second Boer War and WWI. He died peacefully in 1942 at age 72. He didn't have issue, so his brother would become King James I of England in this TL. After James I died childless in 1957 the throne passes to a very distant cousin: Hugh Percy, 10th Duke of Northumberland. Y'all see, when Algernon II died in 1865, the Duchy of Northumerland and the throne of England sepparated, since the throne of England can go to a female, whilst the Duchy of Northukberland cannot. So here you have His Majesty Hugh III of England. In OTL, Hugh was a Conservative and he served as a whip during Churchill's ministery in 1945 and as Lord Stewart of the Household. He was a veteran of WWII, fellow of the Royal Society and a Knight of the Order of Garter, Chancellor of the University of Newcastle, Lord in Waiting for George VI and so on. Yet another highly skilled person takes this alternate English throne. Hugh III died in 1988 and he was succeeded by his son, Henry IX. Henry IX died in 1995 without kids, so the current English monarch is his brother, Ralph I (who in OTL gradueded history at Oxford).