I have done this trip many times by bike, scooter and van over the last few years. Now that I work less so I have more time and freedom, I can make regular trips.
My good ol’ Mercedes Vito van is a V6 3L auto and she flies, I just travelled to the UK and back and she covered 3400 in only 8 days, 2 days each way plus 4 days in the UK. This time I took to the UK 2 Yamaha TMaxs (a very tight fit cos the scooters are wide and long, more so that most motorbikes) and then I returned empty (except of course for loads of French shopping).
I can offer transport for a motorbike or for some boxes or whatever (even a passenger, I have done this already) at a very reasonable price between Italy and the UK. My usual route is Amalfi Roma Orte Chamonix Reims Calais and then over to the UK via P&O Ferries.
Let me know if you are interested on +39 333 8153190 phone or sms or whatapp.