Trans-Atlantic ships

Because the dollar is so week, I figger I can cut down on my time in
England before and after a cruise leaving from Dover by taking ships
across the Atlantic. Apparently this is no longer an easy or
economical thing to do.
My attempts to find information have found some but most of it is
quite old, including a 1997 post in this forum.
I want to travel from Miami after July 20 to arrive in England (Dover
preferred) no later than July 27 and from England after August 14 to
arrive in Manhattan no later than August 21.
I really don't want to fly but fear that I must.
Thank you.