Chiefly used in would you, or could you, Adam and Eve it?, the verb Adam and Eve is rhyming slang for to believe.
Interestingly, in this verb, there is no truncation, contrary to the usual rhyming-slang formation (for example, scooby, rhyming slang for clue, is short for Scooby Doo, the name of a cartoon dog which features in several U.S. television series and films).
This is what the British lexicographer Jonathon Green (born 1948) explains in Cockney, published in the Oxford English Dictionary blog on Friday 17th August 2012:
The original rhyming slang, which was a conscious attempt to mystify the uninitiated, depended on the omission of the rhyming element, for example: ‘Barnet fair’/‘hair’ (1857) to barnet (1931); ‘china plate’/‘mate’ (1880) to china (1925); ‘Hampstead Heath’/‘teeth’ (1887) to Hampsteads (1932); and ‘Sweeney Todd’/‘flying squad’ (1938) to Sweeney (1967). However this was by no means a rule, and there exist a number of terms in which the entire compound is pronounced—hence Adam-and-Eve/‘believe’ (1925), cocoa/‘say so’ (1936), or tea-leaf/‘thief’ (1903).
The verb Adam and Eve is first recorded in Soldier and Sailor Words and Phrases (London: George Routledge and Sons, Ltd., 1925), by Edward Fraser and John Gibbons:
ADAM AND EVE: Believe. E.g., “Could you Adam and Eve it”. (rhyming slang).
The British painter and author Franck Budgen (1882-1971) made this interesting remark in James Joyce and the Making of ‘Ulysses’ (London: Grayson & Grayson, 1934):
When the Cockney is surprised and incredulous and says, “Would you Adam and Eve it?” he slyly spreads his unbelief so as to cast a shadow of doubt on the story of creation in the first book of Genesis.
The verb then occurs in:
1-: Buck Ryan, a comic strip by the British artist Jack Phythian Monk (1904-1976) and the British writer Don Freeman (John Henry Gordon Freeman – 1903-1972), published in the Daily Mirror (London, England) of Saturday 12th December 1942:
YES, THIS LOOKS LIKE AL’S LIST OF INFORMANTS! A NICE JOB FOR SCOTLAND YARD TO ROUND ’EM UP, UGLY!
WELL, WOULD YOU ADAM AN’ EVE IT! WE KEP’ THE TOMMY GUN IN THAT DRAWER AN’ I NEVER KNEW THAT LIST WAS STUCK THERE!
2-: This advertisement for Wisdom, “the correct-shape toothbrush”, published in the Birmingham Gazette (Birmingham, Warwickshire, England) of Wednesday 29th October 1947:
“A bit of orl right!” say Cockney types
See ’ere, these straight-line tufts are just the ticket for getting around them awkward Johnny ’orners.
Would you Adam and Eve it? The tufts are spaced out special to clean between the ’ampstead ’eath.
This ’ere ’arry Randall is bent to fit the old north and south like a turtle dove. The job’s all Chatham and Dover in ’alf the bird-lime.
D’YOU GET IT?
Adam and Eve—believe
North and South—mouth
Chatham & Dover—over
3-: Just Jake, a comic strip by Bernard Graddon (1905-1951), published in the Daily Mirror (London, England) of Wednesday 18th July 1951:
WELL, WOULD YOU ADAM-AN’-EVE IT!! SHE’S BIN SCREEKIN’ AN’ SCREAMIN’ LIKE A PARBOILED PARAKEET—
AND THE BLESSED BULLET DIDN’T EVEN SCRATCH HER POLL!
4-: I’ll Soldier No More: A Novel (London: Victor Gollancz Ltd, 1958), by the British-born New Zealand author Michael Kennedy Joseph (1914-1981):
“Would you adam-and-eve it, now?” said Connolly. “All for fifty-six lousy days in the glasshouse. It’d take more than that to make me shoot meself, I can tell you.”