The historian Tom Standage wrote a book called "History of the World in Six Glasses" which explains the six major drinks that people have drank throughout time. One of these is tea. (Beer, Wine, Spirits, Coffee and Coca-Cola being the other five) I'll try to summarize what he said:
Chinese traditions have always held tea in high esteem. It was used as medicine as well as nourishment. Good tea was even used as currency as some points in their history. It was the official drink of Tang Dynasty. When Europeans began interacting with China (more than just Marco Polo) they would have seen tea as a very big part of their culture.
Tea is easy to make and safe to drink. Any sort of alcohol is fairly complex to make compared to tea. Dip some tea leaves in hot water and BAM. tea. Remember that at this time not all water was safe to drink and some people didn't understand why. They didn't know about bacterias or things like that. They DID know that when water was boiled (coffee or tea) or when it was made in to beer or other alcohol it was generally okay to drink without getting ill.
The Industrial Revolution happened. A popular drink before tea was a morning beer, lunch beer and dinner beer. Generally this beer wasn't too high in alcohol content; it was just enough to get the bacteria from killing you. However, due to the Industrial Revolution, workers began dealing with heavy, fast and often dangerous machinery. Unsprisingly this beer and machinery didn't always mix safely. Tea, becoming more prevelent for reasons below, became the drink of choice among this new working class. It provided a quick, easy break for the workers. Employers approved of the drink because it energized their staff and didn't give them a buzz.
The British, thanks to the British East India Trading Company, basically ruled the tea trade from the Far East to Europe and European Colonies. Because the American colonies were still part of England, Americans enjoyed tea just the same as England. Also at this time, it was getting VERY expensive to maintain finances in the colonies. The French and Indian War (or part of the Seven Years War as it's known in Europe) made the colonies a financial liability. The British crown thought that instead of paying for all this protection out of their own pocket, they should just make the colonists pay for their own protection. How did they get this money? By taxing the ever living crap out of the colonists. Everything from sugar to playing cards to tea was taxed taxed taxed. The colonists a) didn't like paying these taxes obviously and b) didn't like that they didn't have a say in any of this. Hence the "No taxation without representation" slogan every 7th grader knows. We see their protests in the Boston Tea Party.
One way tea was really important historically was in its sparking of the opium wars (vs. Britain) which ended up with a British victory and the subsequent treaty significantly opened up of China for more trade (which it was not interested in at the time). One of China's biggest exports was tea which the British bought a lot of, but China didn't care to import goods from Britain, resulting in a very poor balance of trade. Thus the British ended up selling opium to the Chinese, making many many people addicted to it, which was bad for China not only socially (to have a country of drug addicts) but financially as well. I believe a large shipment of opium was destroyed by the Chinese government and that sparked a British attack and the beginning of the 1st opium war.
China lost and they had to open up trading ports which they were very resistant to before. They preferred to stay relatively isolated with major income from the lucrative tea exporting.
I can't really speak as to why tea was so popular in Britain as I'm not British myself but from my understanding drinking tea daily is imbedded in their culture, thus the need for it would be great.