The British desire to slow westward expansion was a holdover, I think, from the time when the Indians were needed as allies against the French – with the French largely gone by the time of the revolution, and certainly gone after the Napoleonic wars, the only foreign power left to push around would have been the Spanish.

British America would still have expanded across the continent, I think.

There is one problem – that is the two largest economies in the world as we know it. I suspect that if there had not been an American republic the Anglo presence would have reached much past the Blue Ridge. What would be in the interior? An Anglo-Cherokee-Ohio Commonwealth with loose ties to the Empire? Continued Spanish control of the Mississippi and Pacific coast possibly. We got the economy we did because of unique synergies (I’ve been in a few biz meetings lately) possible due to an expansionist American republic.

The British were serious about not expanding the colonies past the Ridge, and honoring treaties with the natives. At the same time settlers were going over the wall, setting up commonwealths, establishing treaties with the Indians. Moses Austin moved clean out of the country and became a Spanish subject .. in St. Louis .. to establish a colony of settlers in Missouri.

I don’t think they could have stopped the migration, but a strong British presence would possibly have halted attempts to gain political control over the Ohio river valley.

It would certainly be a different world, possibly a better one, maybe worse. My feeling is that the British presence would be restricted to the Atlantic coast, depriving the Empire of whatever economic prowess comes from the rest of the continent.