After six years, Alan and Eileen Ransome's marriage is on the rocks and sinking fast, largely because Alan spends more time at work than he does with his wife. In a last ditch effort to save their relationship, Eileen decides to accompany Alan on a business trip to London, booking a slow ship to Southampton in the hope that two weeks together at sea will give them time to patch things up.
As they are about to set sail, some of the other passengers try to convince the Ransomes not to sail on the Lady Anne, offering to buy their tickets for $10K, but Alan stubbornly refuses. During the cruise, the young couple are made to feel unwelcome by their fellow shipmates, all of whom seem to be pensioners. Cooped up together, Alan and Eileen's relationship reaches breaking point, but when his wife suddenly disappears, Alan panics and desperately searches the ship. When he eventually finds his wife safe in their room, he declares his love and vows to mend his ways (amazing how five minutes of sheer dread can make someone completely re-evaluate their priorities).
Things finally seem to be on the up for the Ransomes: even the other passengers are acting more friendly towards them; well, up until the point that the young couple are forced at gunpoint to abandon ship in a lifeboat!
There's a lot of yadda, yadda, yadda in this episode, which tends to make it feel slower than its titular vessel, and Alan and Eileen's bickering is hard to watch at times. Thankfully, the intriguing mystery behind its elderly passengers just about keeps things moving, and the ending, in which the Lady Anne sails off into the mist with the O. A. P.s, never to be seen again, is suitably mysterious -- a final voyage for not just the ship, but for everyone on board, straight into the uncharted waters of The Twilight Zone.