As Dzug indicates, British & Irish citizens don't require a passport to travel between the UK and Ireland (and, of course, vice versa).
All airlines, except Ryanair, currently accept a photo-style driving licence as proof of identity (for security purposes). Some will accept other forms of photographic ID.
To travel with Ryanair you'll need a passport or, if you live or work in the northwest of England, a UK National ID card (£30):
http://idsmart.direct.gov.uk/index.html
Chris