Even if Christopher Columbus never set foot on America, isn't it inevitable that the British Empire would have?

Someone would have.   The western European powers were moving out into the Atlantic more.  For much of European history, the western ocean had been a barrier. Europeans didn't go into it too far.  But by the 15th century, many of them were venturing further afield.  Columbus had the most geographically ambitious plan, to sail around the globe (and they all knew Earth was round at the time) and reach Asia's eastern shore.  But other people had been going out into the ocean for much of the century.  The Portuguese and Spanish had discovered the Azores and Canary Islands out there.  Iberians had also moved down the coast of Africa and into the Indian Ocean.  As these groups did more and more exploration, they would have eventually bumped into the Americas.  It's not like they're that far apart at the closest reach.  In 1500, for example, the Portuguese discovered Brazil when a fleet of their swung too wide while trying to head south around Africa.  Eventually someone would have done something similar, or would have tried what Columbus tried.  The 15th century was filled with figures who were looking to explore the oceans and seas and map new areas.  Someone would have eventually managed to find America

The only reason Europeans could colonize America is because Hepatitis killed off most of the natives. It disease hadn't cleared the way. East coast natives would have fought like hell to stop invaders. 

Plus the remains of Europeans from thousands of years ago  have been found in America. Proving more than just Vikings stopped by America before 1492.  A huge amount of Copper ore is missing from Michigan. The estimate is, it would take 10,000 men 1000 years to dig up the missing copper. The mines are still there and the copper found it's way to Europe.  Natives didn't use copper or use it to make bronze. But someone was traveling to Maine up to 9000 years ago to dig up copper ore. Bronze age European tools tested positive for Michigan copper. So that's proof that Columbus didn't find anything that wasn't found long before he got there. All he did was officially claim land Europeans forgot about. 

the key technology was deep bellied, keeled sailing ships.  With those, enough foods could be carried to sail the Atlantic fairly easily.  after that, it was inevitable

No.  There was no "British Empire" at the time.  Without Columbus, Spain's history in what is now Latin America wouldn't have begun when it did, and European history would have been different.  It's entirely possible, perhaps even likely, that European colonization of eastern North America would still have happened, but it probably would have been a different European power, rather than Britain, and it certainly wouldn't have been the British "Empire", because there wasn't one before colonization.

No.  Empires are never inevitable, people failed. Colonizers were not contained. They're above laws and facts. In 1800 slavery was absurdly evil-Everywhere. You were not inevitable.