Perhaps the most (in)famous of all the Spectrum unreleased games.
Probably the best article on the story behind the game can be found in issue 12 of Crash in The Biggest Commercial Break of Them All (available on the on-line version), which tells the story about the television program which charted Imagine's downfall.
Briefly, Imagine were one of the most publicity-hungry companies of their day. From early 1984 they began publicising their so-called Megagames, Bandersnatch for the Spectrum and Psyclapse for the Commodore 64, and a number of different adverts appeared during the year for the games in the computer press.
Imagine had said that they had reached the limit of the capabilities of the Spectrum and planned to release the game with a hardware add-on which would increase the Spectrum's memory. Various reports suggested that the game would costs anywhere between £20 to £40.
The game though was never finished and Imagine collapsed during about the Autumn of 1984.
On Games That Weren't, Marc Dawson comments that the Megagames had reached "quite an advanced stage and looked incredible"?
The game never appeared despite the fact that Ian Heatherington and Dave Lawson formed a company called Fireiron (nb - I have also seen reports saying this company was called Finchspeed) and planned to release the game for Sinclair Research for the QL either on ROM cartridge or Microdrive.
Some of the programmers who worked on Bandersnatch went on to form Denton Designs and their first game Gift from the Gods
was described as a "direct descendant" of the ill-fated Megagame. The central character in Gift was said to be very similar to the one in Bandersnatch.
The game also made an appearance for the Atari ST in the guise of Brattacus, released by Psygnosis, a company also formed by messrs Heatherington and Lawson. Marc Dawson comments on GTW that Brattacus was a mixture of Bandersnatch and Psyclapse.