It's up to the singer. Some singers are able to rely simply on a sense of their own vocal range to pitch the song correctly. Some people aren't very good at this, and would benefit from using pitch-pipes or an instrument to get their note, while others do this habitually. It's certainly wise, as Sandman suggests, to be aware of the state of your voice, and be prepared to sing in a different key to compensate for an off day, or for the acoustics of the room. If you are not very sure of your vocal range then it would certainly help to know your usual key and to have a reference note. Sandman's advice is sound, although many singers may be able to do this without thinking in terms of named keys.   

However to infer from this that everyone in a UK singaround knows what key they sing in for every song, and can pitch it perfectly, would be very wrong. I often don't know the key even when I am accompanying myself on an instrument - all I need to know is where to put the capo.