London is not actually a cruise port, but is served by the ports of Southhampton, Harwich, and Dover. Together, the cruise port of Southhampton, Harwich, and Dover is the eighteenth busiest cruise terminal, departure point of over one hundred and forty cruises every year from Cunard, MSC, Princess and more to the East Coast, Europe, and the Mediterranean.
Overall London is fairly expensive compared to other ports. Prices are about steady throughout the year. See the diagram below for the average cost per day by month (Cruises only depart from London between January and December).