WI: No James I & VI

How improbable is someone with a distant claim (one of the "would be rejected" ones, perhaps) but enough strength to take the throne doing so and succeeding by the (de facto if not de jure) right of the sword?

Looking at either England or Scotland here.
 
I think the English de la Pole's were extinct by time Elizabeth came to the throne. Henry VIII had done his part to execute a good lot of them (he was always suspicious of those with Plantagenet blood). Cardinal de la Pole was the last remaining male, and he died within hours of Mary. There is Ursula de la Pole who married Henry Stafford and they had a great many issue, but I think his sons were Catholics and got tied up in the business of the Northern Rebellion.

You're thinking of Ursula Pole, granddaughter of George, Duke of Clarence; the de la Poles are a different branch of the family with a confusingly similar name. The Earl of Huntingdon is her heir in 1603.

Yes, the English de la Poles are extinct AFAIK. The ones that weren't executed by Henry VII or Henry VIII fled to France and stayed there.
 
Think this has been done before but:

Will of Henry VIII as enacted as his final Act of Succession as follows:

House of Tudor:

Surviving descendants of Mary Tudor Queen of France, Duchess of Suffolk:

1) Edward Seymour, Viscount Beauchamp (d1612) - regarded as illegitimate by Elizabeth I and her council - but strong claim and has at least six children by 1603.
2) Anne Stanley unmarred in 1603 (senior heir general of Lady Eleanor Brandon)
3) Frances Stanley married 1602 John Egerton future 1st Earl of Bridgewater.
4) Elizabeth Stanley married Henry Hastings 5th Earl of Huntingdon in 1601.
5) William Stanley 6th Earl of Derby

Male preference Primogeniture would give the following line of succession:

Descendants of Margaret Tudor Queen of Scots.

1) Lady Arbella Stuart - unmarried in 1603.

Then descendants of Mary Tudor as above.

That exhausts the Tudor line

Other claimants:
House of York:

Descendants of Edward IV through his daughter Catherine of York, Countess of Devon:
NOTE: it is assumed that Catherine of York's daughter Margaret Courteney only had one surviving child - Lucy Somerset
Her senior heir in 1603 was
1) Henry Percy 9th Earl of Northumberland

Descendants of George Duke of Clarence -

Principal descendant in 1603 was
1) George Hastings 4th Earl of Huntingdon (numerous other relations all descendants of Catherine Pole - daughter of Henry Pole son of Margaret Plantagenet Countess of Salisbury)

There were numerous other Pole descendant from Margaret's younger sons and the descendants of Margaret's daughter Ursula Baroness Stafford.

Descendants of Anne Plantagenet eldest daughter of Richard Duke of York

Senior descendant in 1603 was William Bourchier 3rd Earl of Bath.

Descendants of Elizabeth Plantagenet Duchess of Suffolk youngest daughter of Richard Duke of York.

Edmund de la Pole left one daughter Margaret de la Pole who married in France in the mid 16th century - with issue who would be the only claimants to the claims of Richard of York's youngest daughter.

Descendants of Isabel Plantagenet only sister of Richard Duke of York;
Her senior heir in 1603 was Robert Devereux 3rd Earl of Essex.

House of Lancaster:

The senior descendant of Philippa of Lancaster Queen of Portugal in 1603 was Philip III of Spain.
 
The legal heir to the English throne according to various theories of succession:

Will of Henry VIII

  • Anne Stanley is the most likely heir here, as discussed above. May face opposition, since the Stanley family has been under suspicion for Catholic sympathies.
  • Edward Seymour, Viscount Beauchamp, was generally regarded as a bastard due to the irregularity and lack of documentation of his parents' alleged marriage. But if he can get this reversed or overlooked, he's genealogically senior to Anne.
Male-Preference Primogeniture

  • Arabella Stuart, as discussed above.
Illegitimate Descendants of Henry VIII

  • George Carey, 2nd Baron Hunsdon -- his father was widely rumored to be the illegitimate son of Henry VIII by Mary Boleyn. This is an extremely weak claim, but there is recent precedent for royal inheritance through bastard lines: Henry VII's claim to the throne came through an acknowledged bastard of John of Gaunt, and Henry VIII at one point had been setting up his acknowledged bastard Henry FitzRoy as his heir.
York Heirs

  • The senior descendant of George, Duke of Clarence (middle brother of Edward IV and Richard III) is George Hastings, 4th Earl of Huntingdon. His older brother (Henry Hastings, 3rd Earl of Huntingdon) had at one point (in the 1560s, I think) tried to set himself up as Elizabeth's heir if she died from illness, and has attracted a bit of support before Elizabeth recovered and quashed the discussions.
  • There are some surviving descendants of John de la Pole, the appointed heir of Richard III (descended from Richard's sister Elizabeth, Duchess of Suffolk). I think the senior heir of this line in 1603 is Jacques de Secondat de Montesquieu, a complete non-entity in English politics, as the family has been French for 2-3 generations by this point.
Lancaster Heirs

  • Isabella Clara Eugenia, daughter of King Philip II of Spain, is descended by legitimate line from John of Gaunt on both her father's side and her mother's side. The post-invasion plan for the Spanish Armada had been to put her on the English throne.
I think we can rule out Isabella, Jacque, and George Carey. Anne Stanley's probably the front-runner if the Catholicism rumors don't stick, and Arabella Stuart or George Hastings otherwise. Arabella might try to shore up her claim by marrying one of the other claimants or their heir (IOTL, she eventually marries William Seymour, son of Edward Seymour).

There's also an intriguing possibility of abolishing the monarchy after Elizabeth's death. IOTL, there was some discussion among members of Elizabeth's privy council who opposed James as heir (most notably Sir Walter Raleigh) of establishing a Republic upon Elizabeth's death.

As for the Scottish throne:

  • James Hamilton, 3rd Earl of Arran had OTL been considered heir presumptive of James VI until the birth of James VI's first son. By 1603, however, James Hamilton has long been confined to his rooms as a lunatic, so he may be passed over in favor of his son John Hamilton.
  • Arabella Stuart has a pretty strong genealogical claim based on her descent from the Earls of Lennox, but has little or no native Scottish political support. Her only chance of claiming the Scottish throne would be with English armies at her back.
  • Arabella's cousin Ludovic Stewart, Duke of Lennox inherited Arabella's father's Scottish titles, and could be argued to have inherited the Lennox claim to the Scottish throne as well.

Edward Seymour would be an interesting choice as grandson William Seymour marries Arabella Stuart.

Perhaps would make Arabella claim to Scotland (and hence a re-union of the crowns ) more likely, especially if a regency existed for the Earl of Arran whilst he was incapacitated and the marriage with Seymour was advanced a year or so.
 
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