Getting your history wrong

People (well men) are randy by nature, whilst a woman will try to find a reason to have sex because of the consequences, men usually need only to find a place. In the past, the more money and power you had, the easier it was to have a mistress and one of the forms of birth control such as it was for the nobility was to marry your mistress off to one of your fellow courtiers/men at arms who in order to increase their influence, were quite happy (for a given degree of happy) to tolerate this. it meant that any children were not born bastards and if or when the relationship ended the woman involved had a settled secure place.
No it wasn't perfect and yes there were problems with it, but it's something that was common enough with male monarchs throughout the centuries, power (wealth) and sex often going hand in hand.
Which is why this story in the Mail made me sigh in exasperation, I don't know if it's just the Mail being ignorant or the historian putting modern thinking on a historical situation. Either way they're wrong.
Mail.

King Henry VIII had a secret daughter who should have taken the throne before Elizabeth I, new research has revealed.
Elizabeth Tailboys was the Tudor monarch's illegitimate lovechild who would have changed the course of English history had the King acknowledged her as his at the time.
By rights she should have taken the throne on the death of Queen Mary in 1558, making her the true Elizabeth I and not Elizabeth, the daughter of Anne Boleyn.

Leaving aside the laws of primogeniture and the occasional royal meddling in which the King was given the power to designate his successor legitimacy tended to be the key to which the royal line was maintained. Henry might have acknowledged his son Henry Fitzroy and possibly even planned to marry him off to his daughter Ann (Catherine of Aragon's daughter) but, acknowledged is not the same as legitimate and would have caused major problems (schism) had he not died young probably from the same affliction as his legitimate brothers Arthur and Edward. Male succession aside though, female offspring did not get the same treatment, Ann and Elizabeth, Henry's daughters only maintained power whilst there were no men in their lives. Ann's marriage to the King of Spain was not popular and it's likely she would have been overthrown had the King ever tried to land on English shores to take charge, the later defeat of the Spanish Armada stems from this marriage when Philip of Spain tried to assert his right as King of England by way of his previous marriage to Mary.
There was never any possibility of another Queen Elizabeth ascending to the throne, acknowledgement or not, the very fact Henry did not acknowledge her probably saved her life, look at what happened to Lady Jane Grey after Edward died.
First law of a disputed succession, kill all your rivals, save an immediate heir, Had Mary had a son, (both) Elizabeth's days would have been numbered, an illegitimate Elizabeth's for certain.
I'm pretty much certain a historian would know all this, so I suspect it's just the Mail playing fast and loose with facts again.