"The first generally recognised king of all England was Egbert of Wessex who reigned from 829 - 839 AD"
Oh no he wasn't! (Well it is nearly Panto season).
King Alfred the Great is often held as being responsible for the vision of their being a single King of England but never achieved it in his life (it's one of the reasons why he's the only King called the Great). However it wasn't until his Grandson Athelstan in the 920s that that was actually achieved. Even Alfred is "only" known as the King of Wessex, Athelstan is the first King of England.
And Egbert and his House of Wessex, which includes both Alfred and Athelstan, weren't Danish. That House was allegedly founded by Cerdic who was a Saxon, or British, or part Saxon part British but certainly not Danish.
The Danes came later, and it was them who stopped Alfred being King of England and Alfred and his house had immense problems with them.
King Alfred is also a direct ancestor of the current Queen.
"In 1603, King James I reigned as the first King of all Britain"
That's not as "wrong" as naming Egbert as the first King of England but it's not quite right....
King James in the early 1600s was the King of England, Scotland and Ireland. They were still separate Kingdoms under him, he was never known as the King of Britain.
The first Monarch of Great Britain was Queen Anne when the Kingdom was made in 1707.
The United Kingdom of Great Britain and Ireland came into existence in 1802 and the first King of that Kingdom was George III.
Finally in 1922 we get the modern United Kingdom of Great Britain and Northern Ireland and it's that title, among others, that Queen Elizabeth still holds.
"The following monarchs of England were then generally made up of the French from William I"
William I wasn't French, he was a Norman, a Norseman. He descended from Norse raiders, Vikings, that settled in that part of France and caused so much trouble that the then King of France granted them a large Dukedom on the condition that they leave him alone.
It's also worth noting that William's son Henry I's wife was from the House of Wessex, so the Norman Monarchs claimed descent from both the Norman conquerors of the country and the much older House of Wessex who made the Kingdom of England in the first place. Very politically savvy....
If we're going to take pot shots at them let's at least understand their background, history and claims of legitimacy.