Inevitable from when?
I note you say was Britain's rise as a superpower inevitable- to that question I would say yes, as far as anything can be said to be inevitable. By the time the union was formed the pieces were all ready to fall into place .
And to the other question- it was a bit of both but it was more of a case of Britain controlled a quarter of the planet because it was powerful, than vice-versa.
Its not sitting on huge tracts of land that made a pre 20th century nation powerful, that is quite a modern post-war development. Its economics. British industry and business led the world, British military and diplomatic power was just to support this.
That sounds much more reasonable (the percentage), and yeah.
Although it is interesting that Britain had The Best Fleet Afloat for only maybe a century plus.
Wins of consequence before that, but both before the French Revolution and after the German naval buildup, it was hardly unchallenged.
Sure, it wasn't the undisputed, could beat any two countries navies before tea time, behemoth it was in the 19th century at those times, but it was still the most powerful.
The British navy was the most powerful in the world since.....the seven years war or so? Perhaps even earlier with the Dutch decline. It didn't cease being such until around WW2 when the US took over.
Its lead was nowhere near as big then but it was certainly first among equals.
Quality-wise, I have yet to hear of anyone describing the British army in this period as a particularly elite force, but even if it was, that's a small army. A small army mostly scattered all over this huge, sprawling empire.
Hardly an overwhelming force that can be concentrated on anything without massive wartime effort (and according strain).
The whole army scattered across the world holding down the empire thing is a bit of a myth. The empire wasn't constantly chomping at the bit looking for any chance to rebel and local troops largely defended the colonies with British troop numbers being rather low outside of the officers.
The small British army was by design, not lack of capability. Though the modern government is rather disturbingly changing this and pushing us the way of America's bad side, Britain has traditionally been pretty anti-army. We didn't like having too many soldiers hanging around the country just in case.
If there was going to be a war then we were more than capable of putting together an army.
Or as in the case of the Napoleonic Wars, subsidising somebody who was also an enemy of our enemy to do all the dirty work for us.
There were no land borders ,the government always kept on top of the diplomatic situation and Britain had the navy so there was no need for a big standing army. The lack of such an army contributed to making Britain more powerful, not less- armies are expensive and that we had a good enough navy to not need one really helped add to its myth.