Carriers face heavy fines if they convey passengers without the relevant documentation to enable them to enter their destination country, so it's extremely unlikely that any airline or ferry company would allow your son to travel without a valid passport (which, until such time as we get national identity cards, is the only acceptable proof of identity for travel outside of the UK and Ireland).
If your son's travel arrangements aren't until late in the day, he might be able to get his passport renewed if he can get to a passport office (and then to the airport or ferry terminal) in time. It's essential to have an appointment but the Passport Advice Line operates a 24 hour service (0870 521 0410) so they might be able to find a vacant slot for him tomorrow. See here for further details:
http://www.ips.gov.uk/passport/apply-urgent-wi thin-two-days.asp
Chris