With the absence of the article before term, the phrase end of term is a generic reference to the point which all terms eventually reach. With the article, the phrase the end of the term, the reference is specific, to the term in question, whether it is the current term or some other term being spoken about.
Once again, the "facts on the ground" do not determine what comes out of the speaker's mouth. Speakers present those facts as they see fit; they are not slaves to them.
So I could refer to end of term if I like because this current term is no different from any other term. It too will have an end. Or I can say the end of the term because I have the current term in mind. And I may not be consciously making a choice. Both choices are available to the speaker and the speaker is likely not even to consider why that is so.
P.S. We use "end of term" in AmE as well.