There was only a single one part story in classic Doctor Who - and really that was a prologue for a twelve-part Dalek epic so it doesn't really count. It appears to have not been something that any of the production teams over the years ever considered as a possibility - but I think this little story shows that it possibly could have worked.

The story of this is that Moris Farhi wrote this single part story as a model script without being commissioned by the production office; but it got him a commission for Farewell Great Macedon (where in place of a storyline; he wrote six complete scripts due to his discovered love for the period). It was never seriously considered for production and I don't think it would have fit the era at all; but I really loved the context of this story. It weirdly feels a lot like one of the various short stories that are told and I also really like those; as it fleshes out the experiences of the characters - surely travels in the TARDIS is not all danger and near death. It also feels a lot like those as it is primarily a character piece involving Barbara and a character called Rhythm

The TARDIS crew have spent a prolonged period on the planet Fragrance where Barbara has struck up a friendship with a young man called Rhythm. Repairs to the TARDIS have been completed to the crew are ready to go - but Rhythm has fallen in love with Barbara so asks her to stay. The cultural norms on Fragrance are that love only happens once and if rejected (or if the other person dies) then your life is forfeit and you must also die. Rhythm's parents - who have helped the Doctor repair a key component - demand that they make Barbara stay but the Doctor and Ian refuse; and so as the TARDIS crew depart Rhythm sails out to sea, and appears to set fire to himself and his boat. Its a remarkably dark idea for this era of Doctor Who (and I don't think would have been made) and touches on some interesting themes of love and cultural differences that wouldn't have been covered at that time.

The acting is remarkably good - the desperation of Rhythm's parents and sisters towards the Doctor, Ian and Susan is notably good. The sound design also works as well.

This story isn't for people that want more traditional Doctor Who (with a bigger general peril and villain - where there isn't one here) - but if you like more different things then this is well worth a listen.