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 called "exile's rose;" 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.

Gaoler's Honey

Colloquially called red honey, because, well, look at the picture. This is a more sinister breed. 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.

This 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...
...will prepare and take a drop of this honey, and be transported to a mysterious dream-location called the Chambers of the Heart. It seems visitors to this place may root through others' memories. Which will be painful to the victim. Interesting.

Gaoler's Honey Across the Sunless Sea

As it turns out, red honey 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 is used to create honey, but escapes and drinks the honey containing their memories, they will be fine, though they will get some memory problems. Several important NPCs of Sunless Sea are implied to be addicted to honey as well.