If you're already in a Schengen group country, shown in either dark blue or light blue on this map, you can travel to any other Schengen member state without any passport formalities whatsoever:
http://upload.wikimed...-Schengenzone.svg.png
(Remember though that airlines still require some form of photo ID for security purposes).
If you're currently outside the Schengen area (e.g. in the UK) you require a passport for all international travel (except, for certain citizens, between the UK and Ireland).
If you're a citizen of another country, currently in the UK, you'll either need to renew your passport via your embassy or consulate or (in exceptional circumstances) seek a Home Office Travel Document in order to travel abroad.
Chris