A lot of Americans in this thread seem to be missing the point. The article isn't about the Brits hating it when Americans use those phrases, it's about them hating it when other Brits use them. Brits in general couldn't care less how Americans talk in their own country.
What it stems from is a general dislike of America and American culture. British people get American culture shoved down their throats every day whether they like it or not. American TV, America films, American brands and products, American food, American news, American ways of thinking, American everything, to the point where they have to cling to their own culture in order to maintain their national and cultural identity. Unfortunately, America does not carry positive connotations with a lot of British people, so this Americanisation is unpopular with some. When the rest of their country is being "infected" by American culture, it irritates them when even their own people start acting and sounding like Americans. They reject words and phrases not necessarily because they are "wrong", but because they sound "too American".
I imagine Americans would hate to have another culture forced upon them on a daily basis. Oh and Zee only sounds better to Americans because of their accent.