I mean, claiming the British were world policemen in a manner to what we are does seem a bit silly. Unless your just saying colonialism is world policing. In which case, Britian never reached that level of dominance. The French, Americans, and others were other rival naval powers.
What point do you consider England to have been world policeman? Are you only really considering it so post Nepoleonic War? In that case then, who was the world policeman before then?
It's as
@GoldRanger says. The world's normal state is either a Great Power playing world policeman or several powers jockeying for that position until one comes out on top. I'm not concerned with extreme exactitudes here since World Policeman isn't that rigorously defined anyway. I don't feel like having to argue why every little thing doesn't count because this one detail's slightly different, of course details are different. But let's check the Wikipedia page:
en.wikipedia.org
So first off the term
was applied to the UK by people long before the US filled the role, as I said. Additionally the US was recognized as world policeman around 1945, when the USSR was absolutely a rival naval power so having rivals is not exclusionary.
Before the great age of sail made it possible for ships to travel all over the world obviously there was no
world policeman because, as we'd use the term there, the world didn't exist yet. There was no interconnection to speak of to police, oftentimes nations hadn't even heard of each other at the distances we police today. However everywhere you found clusters of countries and trade to regulate, a policeman would pop up for that area.
When the map of the western world was effectively a map of the Mediterranean and lands next to it, we had the Egyptians acting in the capacity of Mediterranean Policeman and controlling the trade in bronze, up until around the bronze age collapse, after which the Phoenicians became the Mediterranean Policeman, then the Greeks and so forth.