In particular the British Indian army. With Indian troops Britain would have significantly outnumbered Germany, wouldn't it?
Colonial troops fought in World War Two in great numbers. Canada had around 10% of its population enlisted in the military by the end of WW2. (around 1 million soliders.) New Zeeland, Australia, India, South Africa etc all had expeditionary forces that fought in the war.
These forces were deployed to many different parts of the empire throughout the war. For instance Canadian forces participated in the defence of Hong Kong as well as the invasions in Normandy.
Wiki says that the Indian army in particular grew from around 200k troops in 1939 to over 2.5 million by 1945.
The Indian Army fought for Britian in North Africa, and in Italy. But the vast majority of their engagements were against the Japanese who posed a severe threat to India its self through their invasion of Burma
The British did make extensive use of its Colonial forces on all fronts - and there is part of the explanation - Britain fought on several fronts throughout the war and had the need to secure a vast territory as well.
Parts of the Indian army fought in East Africa (against the Italians), Syria (against the Vichy French, Iraq (against Iraqi revolters), North Africa (against the Germans and Italians) and in Italy (against the Germans) as well as in Malacca, Singapore, Burma and India.
Before the war broke out, the Indian army had only 5 divisions that were trained to the standard of modern European forces. While the British tried throughout the war to raise larger Indian forces, they suffered a severe setback when the BEF lost all their Equipment in France when being evacuated in Operation Dynamo in June 1940. What Britain could produce was needed for rebuilding the British army and the fighting in North Africa.
The Indian army also suffered badly in several reversals - the 3. Motor Brigade surrendered in Aril 1941 after being surrounded by Rommel's forces in Libya and they lost about 40 000 men when Singapore surrendered. Durign the Burma Campaign, the Indian 17. Division was all but destroyed, having to abandong almost all its equipment, and other parts of the Indian forces in the region was also badly damaged.
What Indian forces were built after that was mainly deployed against Burma and then partook in the British late 1944 offensive to recapture it.
The British did use the Arab Legion in Syra and Lebanon, the Indians on every front except France, the King's African Rifles in East Africa and so on.
Not using these forces on the western front was mainly because of logistics. It was logical to use troops close to their source of supply and reinforcements, so by the end of ww2, the British had most of the Indian forces in Burma, the King's African Rifles in North and East Africa, the Arab Legion in Egypt and the British army in France.
Troops that were literally colonial - ie not Canadians; Canada was by WWII a sovereign nation - tended to be more lightly equipped, and trained for punitive expeditions and keeping order against unruly tribes, not for meeting the Wehrmacht in set-piece engagements. So famous a unit as the King's African Rifles, for example, had no organic artillery until September 1939, when the 1 East African Light Battery was formed. This was partly because artillery is dang expensive, and partly so the British Army could more easily crush the native auxiliaries in the event of a rising.