The UK and the Republic of Ireland operate an 'open border' policy so, as far as the immigration authorities are concerned, no passport is required.
However, all airlines require valid ID. This varies between airlines - check the relevant website(s). Ryanair's policy is that will only accept a valid passport (expired documents are not valid) or a photocard driving licence. (Nationals of EEA countries which issue national identity cards may also use these cards). Full details of their policy can be found here:
http://www.ryanair.com/site/EN/faqs.php?sect=p id&quest=photoid
Chris