London isn't a cruise port, but is served by the ports of Southhampton, Harwich, and Dover. Together, Southhampton, Harwich, and Dover acts as the embarkation for over one hundred and ten sailings every year from Cunard, MSC, Royal Caribbean and more to the East Coast, Europe, and the Mediterranean.
Sailings departing from London during the peak seasons of winter and summer are significantly more expensive than the the low season of fall. Overall sailings from London are fairly expensive compared to other ports. Check the chart below for the average cost per day by month (cruises only depart from London between January and December).