Try natinalexpress proberly the cheapest
Have done Heathrow Bus Station (near terminal 2) to Southampton Bus Station, then taxi to the Docks. National Express times and prices are on their web pag.
The company I use is called Advanced Airport Cars 0800 028 4 755 and the cost is about £60 one way and about £110 return .....Nei.
Hi, we are arriving in heathrow on the friday night and are staying over night in the heathrow rennaisance hotel (advance booking of approx£60 per room for two people)as this is one of the pick-up points for a coach transfer to southampton pick up is at 13.00hrs,but perhaps your sailing on the friday.