FWIW the last ferry service connecting Hamburg and Harwich closed down in 2002. As to traveling by container ship, as recently as 2019 I saw Hamburg Süd (now belonging to Maersk) advertising classic passages, but I'm guessing those go to China and southeast Asia considering container freight to/from UK would fit on small feeder ships today ;) If you're into the nostalgic aspect of traveling via ships, be sure to visit MS Cap San Diego in Hamburg, a freight ship (now a still sea-worthy museum) from just before the container boom in the 60s, it's absolutely fantastic and highly recommended.

Thank you for the recommendation! I might get a chance to visit during the short few days I'm there :)