Actually, it is not quite the case: the most warmongering country in Europe was the UK since the 1600s (between 16 and 18 times depending on the criterias you use, a war declaration is way less a clear cut decision than you might think). They most often declared war to France, whereas during the same time, France declared war about 13 times (mostly to Spain, Prussia and Austria). There is no single source for those numbers, because some count invasions as war declarations, and some others don't, and some count wars against coalitions as 1 and some detail the exact number of countries involved. If you want to compare that with Germany/Prussia, they declared war about 10 times during the same time. And if you want to know which country was the most declared war upon, it was France (about 20 times), whereas England/UK was declared war to only 10 times. So it would not be far fetched to argue that it was mostly England/UK that was the biggest warmonger of the past.
Britain never tried to conquer all of Europe, but France did.
Also, when the Brits have a revolution (e.g., English Civil War, American Revolution) deaths never get as arbitrary and difficult-to-predict as in the French Revoution.