Prisoner's Honey

The preferred drug of the Neath, discovered on the Surface but now far more popular below ground. It's made from the flowers of a certain kind of rhododendron (probably) called "exile's rose," which is pollinated by the lamplighter bee; it induces a deep sleep filled with lucid dreams of that mystical alternate world called Parabola. If one wakes up before one's mind has returned from Parabola, that will make them honey-mazed - effectively drunk.

Xenophon, an ancient Greek writer, wrote of prisoner's honey (he called it mad honey), but the effects on his Surface soldiers resemble honey-mazing more than honey-dreams.

The Devils created Prisoner's honey on behalf of the Fingerkings, so people would be able to visit Parabola. As part of this deal, the Fingerkings owe the Devils 1/5 of everything they gain.

Gaoler's Honey

Colloquially called red honey, because, well, look at the illustration. This is a more sinister breed, whose consumption allows one to search through others' memories - which is incredibly painful for the unfortunate victim. It's made from a flower that is a cross between the exile's rose and a flower from Hell. It seems the hybrid has existed since the days of the Fourth City.

Both types of honey feature in Fallen London and Sunless Sea - more info below.

Red honey is hellish for sure; it has been suggested that... (FATE-LOCKED CONTENT SPOILER)
...a contaminated batch made the Empress's children into monsters. (See The Shuttered Palace and the Empress's Court for more info.)

Those seeking their Nemesis...
...may prepare and take a drop of this honey, and be transported to the mysterious dream-location called the Chambers of the Heart, where visitors may root through others' memories.

Gaoler's Honey Across the Sunless Sea

The red honey that is not gathered in Hell is produced on the Isle of Cats by the Pirate King, Leopold, who himself is a honey addict and is mentioned in one of Fallen London's sidebar snippets. The people whose memories are used to create the honey are kept locked in cages, and are almost comatose due to the amount of pain they are experiencing. Leopold has two important followers: Zaira, the Lady of the Cages (who leads the Melliferous Sisters in gathering the honey) and Isery, the King's Claw (who is gender-ambiguous and features in Fallen London as well).  It is said that if a person's memories are used to create honey, but they escape and drink the honey containing their memories, they will be mostly fine (though they may still have some memory issues). Several important figures across the Sunless Sea are implied to be addicted to honey.