Let's also not forget that while the Prussian army had twice as many men as Wellington had British soldiers, the allied force he commanded was still the bigger of the two armies.
Also remember that the Prussians got their arses handed to them in the battles before hand, meaning they were initially having to retreat, and that it was Wellington taking on the bulk of the French army that gave the Prussians time to regroup and subsequently deliver their devastating assualt on the French flank, that ultimately won the day and defeated Napoleon.
It was a victory that couldn't have been done without Wellington, hinging on his choices, his choice of ground to fight on, and his gamble that his allied forces could hold and bleed Napoleon long enough for the Prussians to get their act together and land the killing blow with fresh reinforcements against exhausted enemies.
It was far from a soley British afair, but it was still the plans, actions and decisions of a British man that won the day, so there is a damned good reason as to why history records it as a British victory.