Protestant England has, arguably, had a disproportionate influence on world events in the past five hundred years or so. Protestantism is a much more decentralized form of religion than Roman Catholicism, and this decentralized structure favors individualism, initiative, creativity and democracy. The first modern democracies were in Protestant Switzerland, the Netherlands and Britain. Subsequently, democracy was adopted and expanded by the Protestant United States, a transplant from Great Britain. The more aggressive development of the British thirteen colonies as distinct from the rather limited exploitation of French North America and the Empire of New Spain might well be attributable to the cultural differences between Catholicism and Protestantism, and the effects these have on entrepreneurial endeavor, in general. The Protestant work ethic is fairly well accepted among many historians, as a real social phenomenon. Arguably, as well, more decentralized systems may favor scientific and technological advances more than more autocratic government control.
But, curiously, in this particular case, all of this really rests on the fifty-fifty chance of a roll of the dice -- healthy boy, or healthy girl? Because in the early sixteenth century, men were much more important than women, socially. And, if Henry VIII had had one or more healthy sons from Catherine of Aragon, he would have had no need to seek a divorce from the Pope, because he could have rested secure in the knowledge that his own dynasty, and English independence, were assured.
Now, these events occurred at a critical period in world history. In particular, Spanish power was at a maximum, in Europe, and worldwide. Charles V was emperor of New Spain, master of the entire Western Hemisphere, he was Archduke of Austria and Holy Roman Emperor, making him master of most of Europe, and he had sacked Rome and made the Pope his personal prisoner and vassal. England and France remained independent, but, in the case of England, this was only with great difficulty. And, with only a girl as an heir for Henry VIII, England would almost certainly have become a part of the greater Spanish Empire worldwide. And, this was something Henry VIII would not tolerate, under any circumstances. Even if it meant creating his own religion, a kind of intermediary between traditional Roman Catholicism and Lutheranism, which is precisely what Henry VIII did.
So, if Henry VIII has a good healthy son or two by Catherine, no Anglican religion. And, within a generation or two, Spanish power has subsided sufficiently that there is no particular need for it, in future, to maintain English independence from Spain. So, England, remains Catholic, forever. Like France, Spain and Italy. So, what's the world like, now?
I would say, first of all, it's much less democratic. There might be no major democracies in the world at all. The great Imperial Autocracies of France, Russia the Ottoman Turks and China are dominant worldwide. Secondly, it's rather less populated. Worldwide population might be only a tenth what it is now, and indigenous populations would still be large and possibly dominant in much of the Americas and Australia. Thirdly, science and technology are perhaps a century or two behind our current levels. All because of a fifty-fifty roll of the dice!