Before you could say Jack Robinson
In a very short time; suddenly.
It would be pleasing to be able to point to a historical figure called Robinson who was the source of this expression. Regrettably, we can't. It could well be that there was an actual Jack Robinson who was reputed to be quick in some way, but, if that's the case, any reliable record of him has disappeared. It is just as likely that Jack Robinson was a mythical figure and no more real than Jack Tar, Jack Frost or Jack the Giant Killer.
It is known that the phrase was in circulation by the end of the 18th century as Mme. Frances D'Arblay (Fanny Burney) used it then in her romantic novel Evelina, or the history of a young lady's entrance into the world in 1778:
"For the matter of that there," said the Captain, "you must make him a soldier, before you can tell which is lightest, head or heels. Howsomever, I'd lay ten pounds to a shilling, I could whisk him so dexterously over into the pool, that he should light plump upon his foretop and turn round like a tetotum."
"Done!" cried Lord Merton; "I take your odds."
"Will you?" returned he; "why, then, 'fore George, I'd do it as soon as say Jack Robinson."
Sir John Robinson was the Constable of the Tower of London for several years from 1660 onward. Some have suggested that he was the source of the phrase and have bequeathed him a reputation for hastily chopping off people's heads. There's no evidence to link the phrase with Sir John, or that he was in any way unusually quick in dispatching the Tower's inmates. That suggested derivation also fails to account for the hundred year gap between Sir John Robinson's career and the first appearance of the phrase in print.
The lexicographer Francis Grose had the advantage of working around the time that the phrase appears to have been coined and he believed that the derivation related to an actual person. Grose's 1811 edition of the Dictionary of the Vulgar Tongue defines 'Jack Robinson' thus:
"Before one could say Jack Robinson; a saying to express a very short time, originating from a very volatile gentleman of that appellation, who would call on his neighbours, and be gone before his name could be announced."
The lack of any detail about Jack Robinson beyond being a 'volatile gentleman' doesn't encourage any confidence in that account.
See also: 'Jack' phrases.