London isn't a cruise port, but is served by the ports of Southhampton, Harwich, and Dover. In total, the cruise port of Southhampton, Harwich, and Dover acts as the port of departure for around forty-five cruises anually from Celebrity, Norwegian, Carnival and more to Europe.
Overall cruises from London are rather expensive compared to other ports. Check the chart below for the average cost per day by month (Cruises only depart from London between April and November). Cruises scheduled from London during the the peak season of spring are significantly more expensive than the the low season of fall.