"The phrase or saying, all my eye and Betty Martin means that something is total and complete nonsense. It is found in British English from the eighteenth century on, but is hardly known today. It is first recorded in a letter of 1781 that was collected in W H Hutton’s Burford Papers. We also know that all my eye, with the same sense, is at least half a century older."
And more (ultimately fruitless) etymological conjecture over at World Wide Words.