Tea is essential to Irish hospitality.
The service of tea in an Irish house is not accompanied by any particular formalities, and it does not require any other comestibles -- but it must include the offer of milk and sugar. (Technically, sugar is offered; milk is requisite.)
and for the morningtime break at work.
I know at least one Irish man who would forgo the cup itself if he hadn't milk to put in it and there isn't an Irish person alive who'd not look at me funny because I drink it black.
The question "sugar?" if you don't already know or remember should elicit a response in the form of a number.
At work, teatime involves a good little bit of something to eat as well. In fact, food is implied in "a cup of tea," at work.
A friend of mine once told me that the Irish would traditionally consider coffee to be a "Nancy-boy's" drink.