Dunkerque is a major port town at the Channel with ferries to Dover (norfolklines – crossings every 2 hours). It is less busy than the Calais-Dover route. Both the Calais-Dover boats and the Dunkerque-Dover boats do not charge for extra passengers in vehicles. Tell drivers this and ask for a lift with them. The Dunkerque-Dover ferries do not take foot passangers so the only option is to a get a lift with a vehicle.
Calais-Dover ferries may be a better choice, as they allow foot passangers. This gives you a backup plan in case you don't get a lift. Foot passanger tickets cost around £15 (20 Euros). Calais also has a ticket office especially for tickets bought on the day, which is good place to ask drivers for a lift.
Once you are on the ferry, it is an excellent idea to ask around for a lift. It far easier to do this than to wait hitchhike when you land. The best tactic is to approach individuals directly and say "Excuse me, sorry to bother you. I am trying to hitch-hike to [destination]. I don't suppose you could give me a lift in that direction?" Most people on the boat will speak English. Do not try to get a lift by standing at the stairs from the car deck with a sign. It does not work well.