Hi! There is a transfer that Princess is providing from Victoria Station. You have to be there before 11 a.m. in London I am told by Princess Cruises.
We are going into Heathrow and have "Air At Ease" picking us up and taking us directly to Southampton hotel. They will also take you straight to pier. You can call them and make arrangements 011-44-2380-733157. They were referred to us by our Southampton Hotel. It cost 60 pounds, for two persons (double check on that) and the vehicle can handle 2 more with luggage.
When are you going there? WE ARE GOING THERE ON 9/3 It would be great to find someone to share expense!