Originally Posted by LH738

Your advantage is that you start already at terminal 4 or terminal 1/2/3 where you will have no problems to board with your luggage. The tube will get fuller and fuller. So place your bags next to the exit (I don't know if left or right side). Normally many people leave and board the tube at Hammersmith station. I would stand up at Hammersmith station and wait the remaining stops until South Kensington. I would go with the tube - even if the tube gets very crowded you shouldn't have problems with your bags.