The world was a very poor place in the 1880s. The per capita GDP of Britain was much higher than the world average. The fact that, as you rightly claim, she could not provide decent living conditions for much of her populance is immaterial; what is important is that Britain at that time was doing much better on a per capita basis than the rest of the world (except Germany and the US).
So using the per capita GDP standard, Pakistan, India and China are all ineligible for claiming world power status, as none of these countries have a per capita GDP which is equal to or greater than the world average. The world refers to China as a great power due to absolute numbers, and not due to the excellent life it is able to (not) provide to its people.
A slightly more useful yardstick for measuring well being of people would be the Human development index. In this, only China has a slightly higher HDI than the world average, and so can say that it is somewhat meeting the world's expectations. India and Pakistan are nowhere in the picture on human development front, although India is making slightly better progress than Pakistan.
So in other words, your Victorian England reference is a wrong analogy.
By the way, can I get one of these ThinkTank logos for my profile? It might look cool!