I am drinking tea
is a perfectly acceptable and grammatical sentence. Tea is a beverage, you drink it. It is moreover very common to have a tea break mid-morning. You could have also said,
I am having a cup of tea
Which sounds awfully British, and quite refined.
If instead you have renounced the ancient art of brewing loose tea in a teapot, and like me are now dropping a single tea bag in a chipped mug, filled with freshly boiled water, and waiting exactly one minute before fishing it out with your teaspoon, then say:
I'm having some tea.
If you say this before 4 p.m people will always understand the beverage. If you say this from 4 p.m and onwards, some British folk might think you are having a light meal, indulging yourself with Devon scones and lashings of clotted cream and jam. But only a few people. People rarely do that sort of thing at home nowadays, it's more likely a couple of rich tea biscuits, or if you're lucky, chocolate digestives. Mmmm....
The friend who commented “What an English …” didn't get to finish their phrase, for whatever reason, they probably meant: “What an English thing to do”
However, if “What an English” was indeed the complete statement, then he or she was at fault. English is both an adjective and a noun, but when it is used to refer to the people of England the definite article is normally used
The English, e.g. The English are a nation of tea guzzlers, every day they drink a 165 million cups.
If referring to the language, the article is not needed, e.g.; English is the third most widely spoken language in the world today.
Then there is the third meaning, english—note the small letter—which is the spin on a cricket ball.
From the context, it is clear that neither of these three meanings were being used.