London is not a cruise port, but is served by the ports of Southhampton, Harwich, and Dover. Together, Southhampton, Harwich, and Dover is the nineteenth busiest cruise port, boasting about one hundred sailings annually from Norwegian, Carnival, Royal Caribbean and more to Europe.
Sailings leaving from London during the the peak season of summer are considerably more expensive than the the low season of winter. On average London is moderately affordable compared to other ports. Check the illustration below for the average cost per day by month (Cruises only depart from London between February and December).