Actually it's not just the English that don't have closets in their homes. Generally European houses are lacking the closet space that Americans desire.
Mainly this is because they didn't have the amount of possessions that we have today. Actually after World War II, American and Europe went in completely two different directions which explains a lot about their culture.
Before the war, American houses didn't have closets either. America decided that they need to keep all the manufacturing plants open to keep people in work so they needed to make people buy things. It's in our culture to own things, consequently we needed the space to store all our stuff. That's why we work longer hours in order to afford all the stuff we buy. I am not saying its wrong I am just stating the differences in the culture.
After the war, Europe went in the direction of working less and spending their money on experiences such as holidays, going out for a pint with a mate and doing stuff.
The more that the British are influenced by the States, the bigger the houses are to hold the stuff we have, and you will find newer houses will have closets. You can still get wardrobes from the base so don't worry too much about this.
