Experience As Of May 2023 at Southampton:
Like other Princess B2B, you will get a letter with a "Transit Card". The letter said to just have the Transit Card, Medallion, and Govt. Issued ID. (prefer Passport) when coming back to ship. Remember you will have the SAME single Medallion for both legs. The Medallion gives only the Embarkation Date -- not the End Date.
Reality: A "few" of the British Port Officers at the re-entry "Entrance" were a little more cautious! They looked at the date and said the Medallion had expired! We explained. The Officer had a Printed List of all Transit Passengers and he compared our names on the Medallion with that list. Just took extra 10 minutes. Most of the Transit Pax were just allowed in with just the Transit Card and Medallion without the extra verification! Depends who was checking at the re-entry.