The first thing you have to realize about standing armies are that they are expensive, and thus states tend to not like having large amounts unless they are necessary or unless they are in a war that requires them. Thus the size of a country's army is not at all a function of their size or population, but rather their necessity.

The Soviet Union required a large standing army because it is a land power, it is vulnerable to invasion from almost every direction and has had historical experiences of getting invaded by such (Germany, France). In addition the Soviet Union was also after WW2 engaged in a massive cold war with the United States which required constant power projection and military buildup, further necessitating a large land army.

In stark contrast, the British Empire is primarily a naval power. Britain was an island, the last time Britain has been properly invaded was during the early middle ages. Britain was also not in any kind of war that required such a large standing army for most of its existence. Colonial policing and adventures do not require large armies. To put it bluntly, Britain did not have a large army because it had no need of one.

Now, what the British Empire did have a need of was a large navy, and so appropriately it had the largest and most powerful navy in the world at the time. In addition, what the British did have was an extremely well trained and equipped professional army, because that was what was best suited to police and govern that kind of far flung maritime empire.

The War That Ended Peace: The Road to 1914 by Margaret MacMilan had an excellent analysis of why the British army was so small in comparison to all the other contemporary European powers.