For nearly the whole of human history, the standard of living did not move. A peasant in Roman Gaul, a peasant in medieval England, and a peasant under the early Stuarts lived at roughly the same material level, because any surplus a society produced was eaten by the mouths it then fed. Good harvests bought more babies, not better lives, and population climbed back to the edge of hunger. Economists call this the Malthusian trap, and it held without exception. Then, in a damp corner of England between about 1760 and 1840, it broke. For the first time, output per person began a sustained rise that has not stopped since. That is Britain's hour of glory, and it is the most consequential thing any country has ever done.
What makes it even more astonishing is realizing how total the ceiling had been. Rome at its height was magnificent, and a Roman senator commanded luxuries beyond a medieval king. But Rome never lifted the floor; the ordinary Roman was no better fed than the ordinary Sumerian two thousand years before. Empires before Britain grew by conquest, by adding land and people and tribute. They redistributed wealth without creating much new per head. The improved steam engine that James Watt patented in 1769, the spinning jenny and the water frame, the cotton mills of Manchester drawing in abundant coal and iron, did something no conquest had: they made a unit of human labor produce far more than before, and kept making it produce more year after year. Britain did not take a larger slice. It baked a larger loaf, and then learned to keep baking. It turned history, the capitalism it gave power to made wars of conquest impractical for gathering wealth (although that would take ~200 more years to realize).
The potential objection is that none of this was British genius, but British luck. The coal was where it was. The empire supplied cotton and markets. The timing was fortunate. Much of that is fair. The question worth asking is not why Britain rather than France or China, which is a quarrel about coal seams and contingency. Why not Rome when it had the British islands? Regardless of reasons, it was Britain that started and sustained the Industrial revolution. What Britain proved was that the law could be broken, by some society, under some conditions, at least once. After that demonstration the rest is detail. The fire need only be lit in one place to spread, and it did, from Lancashire to the world.
That is why this dirty, smoke-choked, deeply unequal half-century outweighs the navy and the Parliament that Britain is usually praised for. Honestly, for Britain, is very hard to choose an "hour of glory" since, as a country, they have several achievements to be proud of. Sea power and representative government were achievements, but other nations had also had them. Escaping subsistence was reached for by none, because none had imagined it could be reached. The modern world, with its rising lifespans and its assumption that children should live better than their parents, begins in those mills. Britain's proudest hour was the moment a society stopped merely surviving and started, for the first time, to compound.