The Showtime series The Tudors is not exactly historically accurate (the Netflix description is 'historically loose but visually lush') but it does incorporate numerous real historical events and people.
In the first series a number of characters die from the 'sweating sickness'. This disease is real and its causative agent is still debated. It had a very rapid onset and its victims could be dead within a few hours following a very high fever.
A 1998 paper suggested that this disease might have been a Hantavirus although others remain unconvinced.
Like Bubonic Plague there is no doubt that a devastating and rapidly fatal illness did appear in England in the late 1400's and early 1500's but in this case it is even more mysterious. The disease was last seen in England in 1578.
Incidentally the Tudors is inaccurate in ascribing the death of Henry's bastard son to the sweating sickness at the age of 5. In real life he died of Tuberculosis at the age of 17. (I'm guessing they did this to foreshadow the later appearance of the disease). However, and I can't remember if they mention this or not, Henry's older brother (Arthur) did die of the sweating sickness at the age of 15. It was Arthur's widow (Catherine of Aragon) that Henry then takes as his first wife to maintain the alliance with Spain. It is then the inability of Catherine to give Henry the son he desires that leads to the whole rest of the saga (the six wives, the two beheadings etc etc).
So without the sweating sickness Henry would not have been king, England would not have broken from the Catholic Church and pretty much the rest of English and European history would have been different.