The term "government" has multiple meanings, but the most direct and common meaning is for the entire apparatus of state power, literally "the instrument which governs". This is true in all places that speak English, the United Kingdom included.

In the United States, we use the term "administration" to refer to an executive, his cabinet, and other associated officials. However, we still recognize the (not-so-subtle) distinction between the administration and the government as a whole; our government, as yours, is divided into three separate branches, and then again into many departments, agencies, committees, circuits, districts, and other subdivisions thereof.