We are huge fans of Brittany Ferries (no personal links); having now taken the 4/4 on 8 return journeys eiher to France or Spain. In our experience, they take exceptional care of "classic" cars. Photo below was taken by Jays when boarding at Portsmouth, en route to the 2012 Le Mans Classic. (Note the lovely Lotus VI in front of Jays car - our 4/4 is the regal red one)
Back in 2012 we did Portsmouth to Bilbao (a long boring haul in a wet early July) and then back from St Malo to Portsmouth...went as a car and no problems with ground clearance etc....only challenge was escaping the car deck as lots of people crowded round admiring and asking questions!