E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
All my Eye (and) Betty Martin.
All nonsense. Joe Miller says that a Jack Tar went into a foreign church, where he heard some one uttering these wordsAh! mihi, beate Martine (Ah! [grant] me, Blessed Martin). On giving an account of his adventure, Jack said he could not make much out of it, but it seemed to him very like All my eye and Betty Martin. Grose has Mihi beatæ Martinis [sic]. The shortened phrase, All my eye, is very common.