Firstly, if we're talking about the UK, let's get rid of the Americanisms: they are TAPS, not FAUCETS
You are requested to report the ATIS information to the Approach function at the airfield. Often this is indicated on the JEPPS/AERADS as Approach or Approach Radar or Director.
At those airfield where there is a local ZONE control (e.g. Jersey Zone) you usually wait until the next function (Approach) before passing the information but sometimes they have the positions combined, so you can't win!!
Do not pass 'Boeing 767 with information Lima' on first contact with London Control even if you have picked up the ATIS whilst still over France!!