So you have to prove you are British. Does having a UK driving licence prove you are British?
I lived in Dublin for two years and have visited Ireland subsequently on many occasions. I have never taken my passport with me.
On arriving at Dublin Ferryport or Dun Laoghaire, merely answering the question "What nationality are you?" in a vaguely British accent will gain you entry.
At Dublin Airport (since the new border posts were installed) I've found that simply handing over my driving licence will gain entry. Before that, you could just walk on by.
The
FCO website says:
"Ireland, along with the UK, is a member of the Common Travel Area. This means that British Citizens do not require a passport to visit Ireland. However, Irish immigration officers will check the IDs of all passengers arriving by air from the UK and most airlines will not carry passengers to and from Ireland unless they have seen satisfactory photographic ID before boarding"