I drove from Scotland to the French/Italian border without being asked to show my passport, and I suspect that was just 'cos the Italian border bloke was a bit bored (top of the Alps). Wasn't asked for it again all the way round Italy, Slovenia, Austria, Germany, Holland, Belgium and France. So, technically, yes you can travel UK-France with no passport. However at airports a passport is the de-facto method of identification (even when getting on UK domestic flights, for example) I'd be very surprised if you manage this OK. I did once fly from the UK to Eire without one though....