Green’s Dictionary of Slang

bogey n.⁴

In phrases

no bogey [? ext. of SE bogey, an evil spirit]

(UK Und.) telling the truth.

1899		Newcastle Courant 18 Nov. 5/2: ‘None o’ your bogey, y’know,’ said Bob. ‘Would I kid you now?’ Jim cried.
1943		R. Llewellyn None But the Lonely Heart 318: But I’m all right. No bogey, Ma. Straight up.