re: How were the British so successful militarily?

Look at most wars they fought. It was rare that Britain fought equal rivals (France, Germany, Russia) over their one of the equal's home territory.

Many of Britain's battles were against much less sophisticated nations (in terms of guns, ammo, weapons) for territory that would help them extract natural resources and crops. It's not hard when you bring a gun to a knife fight.

Even then there were plenty of awful defeats due to utterly clueless generals promoted based on friendships and the old boy network. Just because the sun never set on the British Empire does not mean there weren't frequent defeats in places like Sudan, Afghanistan, South Africa, United States, etc...