score:18
General case — yes, you can travel from the UK to France with just a national ID card. If you have one, that is. The UK does not issue ID cards to its citizens, so if you’re Her Majesty’s subject you’re out of luck. Passports and national ID cards are the only documents which are valid for travel.
On the other hand, many other documents that are valid as IDs are not valid as travel documents; these include, for example, drivers’ licenses and residence permit cards.
Upvote:4
When you say can get there do you mean 'are legally allowed to' or 'have a good chance of sneaking through without being checked'? If the former, then probably no, since that's what a passport is for; if the latter, a ferry may be the best bet, or you could try throwing yourself on the mercy of the Customs officer at the airport/station. I've known both to work, but not reliably; bear in mind also that even if it works, you've got to get back into Britain later.