@Doorsopen,
I think the constituents of "the modern world" are self-evident. Its an observable continua of history and geology. Only interpretation is open to most observers, very few are in a position to make real and calculable impact on "the modern world".
Historically, the United Kingdom defeated France, Spain, Portugal and the Dutch in their bids to further dominate the Western Hemisphere. Its true culturally those non-Anglican influences still survive in the Western Hemisphere, but politically they have long been out of the picture, leaving a vacuum with the only remaining ties being lingual and cultural similarity. Britannia absorbed the rest into its empire, like the Canadian French for example.
What Britain left for the French and the Spaniards, Britain's child the United States took in the Louisiana Purchase and the Spanish American War of 1898, and the USA filled the vacuum left by the Spanish by taking rich territory in the Mexican War.
Spain even lost the Philippines in 1898, making the USA a World Power.
Geo-politically the Anglican influence is unequalled.
Take also for example, the current state of Middle East. The UK and it's children nations have literally defined the Middle East. Britain drew the borders early in the last century. The United States and United Kingdom were the driving force behind the creation of the United Nations and Israel.
In the Middle East they look upon the Crusades as if it happened yesterday.
Science has a diverse foundation dating back to the ancients, however since the explosion of scientific and technological advances the West has led in both endeavours.
Who has led the West during the Industrial Revolution, and the revolutions in Science and Technology? ...It's been English speaking people, with the exception of some fields, such as Physics where the Germans did dominate in the 20th Century.
Even so, most of the German brilliance was absorbed by the West and the Communist Bloc.
Medicine, Education, and Economics have also been dominated by the West.
Many cultures, and I dare say ALL cultures have laid bricks in the construction of the modern world, but the English speaking sphere has undoubtedly built upon those layers in an unrivaled manner.