Well that collection of answers must have confused the questioner!
The simple answer is that British citizens do NOT require a passport to visit the Republic of Ireland. (There's an open land border between the two countries after all).
However the security requirements of airlines and ferry companies (which are completely separate to the immigration rules of Ireland and the UK) vary. Ryanair, for example, will ONLY accept a valid passport as proof of identity, whereas Aer Lingus accepts a wide range of ID documents:
http://www.aerlingus....portsvisas/#d.en.1505
Chris