This is going to be a challenging answer. One reason why Orwell might have written "A Nice Cup of Tea" might be due to the fact that Orwell loved tea. His experiences in growing up in India and Burma might have helped develop his love of tea, and being a British subject, the love of tea is something that is taken as an issue of national pride. Notice the opening lines of the article:
If you look up 'tea' in the first cookery book that comes to hand you will probably find that it is unmentioned; or at most you will find a few lines of sketchy instructions which give no ruling on several of the most important points. This is curious, not only because tea is one of the main stays of civilization in this country, as well as in Eire, Australia and New Zealand, but because the best manner of making it is the subject of violent disputes.
It is evident that the discussion of tea is something of a national issue for Orwell, and does reflect his love for England. While nothing is simple for a thinker like him, Orwell did possess a love of England, and a patriotic spirit that, while not following conventional appreciation, exalted love of nation. Tea is certainly a part of that. Additionally, Orwell went through a great deal of trouble in importing tea to drink personally and had many feelings about it. The article might simply be a reflection of one of his passions: Drinking and preparing tea.
To try to extrapolate a deeper meaning is futile because Orwell is too darn complex and if one thinks they have "figured out" Orwell, they are sadly mistaken. Having said this, I will prove my own futility by suggesting that the article's context might be a desire to hold on to some level of normalcy, routine, and protocol in a world that has seen such elements pass into something not recognizable. The article is published in 1946, and the aftermath of the Second World War was beginning to be recognized. Europe, as a continent, was broken and fragmented, as the Iron Curtain began its demarcation. The ushering in of the Atomic Age and the race for nuclear proliferation began to emerge. The world itself greeted 1946 with an unsteady calm: Not knowing what life after Hitler was going to be like, but also knowing that the memories of such an experience like WWII would not soon be forgotten. In such a domain of uncertainty and doubt, rising from a period where "mere anarchy is loosed upon the world" and "the best lack all conviction while the worst are filled with passionate intensity," perhaps Orwell's discussion and strict adherence to the rules of making and consuming tea are an attempt to make some sense out of a world where there is little of it. The diction and tone of Orwell's article is one of exactitude and demand: There is little in way of ambiguity in how to prepare "a nice cup of tea." Perhaps, this might be the only clarity present in a where ambiguity and imprecision reigns.