"Irish" is the call sign for the Irish Air Corps (not Aer Corps, unless you prefer the gaelic Aer Chor na h'Éireann).
Normally it's only used on flights that will pass through non Irish controlled air space (flights remaing inside Ireland use a type identifier as their call sign) and the tail number of the aircraft is used as the flight number.
Most likely the AC you'll pick up using the callsign in the UK will be one of the three Ministerial Air Transport Sqn aircraft, # 240 (Beechcraft Kingair 200), #251 (Gulfstream G-IV), or #254 (Learjet 45), identified as "Irish240", "Irish251" or "Irish254" respectivly. They will, most likely, be transporting Irish cabinet level politicos (unless they append Victor to the end in which case they have either the Taoiseach (pronounced "Tea-shock", Prime Minister) or Uachtaráin (pronounced "ook-tear-on", President) on board).
These aircraft, along with the AW139's of 301 sqn also carry out patient transfer roles between hospitals in Ireland and the UK. The AW139's carry tails #'s 274-279 inclusive and will use "Irish" callsigns on those missions.
JAS