Britain also had the ability to send troops from British India if needed.
But we forget that any war would not just be limited to the Pacific Northwest and would soon encompass both British and American forces in the Atlantic.
That was reason neither country wanted to fight a war.
Sending troops across the entire Pacific Ocean isn't easy or cheap. And don't forget that the Indian Rebellion happened in 1857, before that the Indian troops were EIC, not British army. And even after that, troops sent from India are troops that aren't being used keeping India down. The real theater would of course be the Great Lakes and over the American coasts. And Britain would have to send a force easily as large as the Crimean expedition. This would be a wildly unpopular war for both sides, too, so it would most likely be undersized forces clumsily capturing undefended stretches of wilderness with the occasional field battle around fortifications that handily defeat the attacking force. There would be a naval battle(my money is on the British) around Vancouver Island or San Francisco and the winner would occupy Oregon Country and a settlement would happen.