I had to think about this for a while before responding and after giving it some thought, I have to give the prize to the Romans. Considering the distances they had to cover with the technology, methods of travel used, supply lines, and communications with the central government and the logistics nightmare that had to be, they were most effective.
The Roman Empire stretched from Britain, across Europe, the Mediterrrainean and middle east. Not only were these lands conquered, they were administered and governed under Roman rule.
I would have to give Ghengis Khan's roaming hordes a close second in military effectivness. I also have a fascination with the Scythians and their methods although little is really known about them.
The Brits, other than having to fight against France, a comparable military power, and defeating the Spanish Armada, never really picked on and defeated anyone their own size. The British Empire established itself in nations that were fairly primitive in culture, economics and military sophistication. British colonies in places like Africa, India, and Malaysia were countries which internally were divided by tribal rivalries. That would leave them suseptable to conquest by anyone with a crude level of sophistication. Furthermore Britain was never able to win a major conflict in the 20th century without outside help. And if the Germans had launched a ground invasion on Britain in combination with the blitz, Britain would have folded and more than likely would be speaking Deutch today.
I do have to give credit to the British naval forces. It was probably due to Britain's naval capabilities they were able to maintain their empire as long as they did.
France was an effective military force and led the world in military technology until the last Napoleonic War. Then it seemed to slide downhill from there. But they did invent smokless powder and changed the face of small arms warfare.