SailRail offers a ticket from any mainland UK station + ferry or fast ferry + train to any station in Ireland.
You can cross from Cairnryan to Belfast, from Fishguard to Rosslare, Liverpool to Belfast and Holyhead (Anglesey) to Dublin.
Train and ship to Dublin costs up to £41.00 per person each way in advance or £46.00 if Advance sold out/buying on the day. Train + ship + train to Cork, Limerick, Galway, Sligo or Tralee costs up to £62.50 per person each way in Advance or £67.50 if Advance sold out/buying on the day. That’s a max of £92 per person to Dublin and max of £135 per person to Cork, Limerick, Galway, Sligo or Tralee from anywhere on UK mainland.
There’s a brilliant website which explains everything you would ever want to know. Ferry or fast ferry, which side of the train to sit to get the best seat, upgrades and cabins onboard etc etc. A real mine of information.