"I don't want you two getting up to any how's-your-father while we're out!"
However, a father with more than one daughter couldn't be everywhere at once. Thus, a suitor having a discreet vis-a-vis with his beloved would cautiously ascertain her father's whereabouts by asking, 'And how is your father?' If her father was currently under her skirts, she would glance downwards and reply, 'My father is very well, thank you, and as alert and vigorous as ever, and maintains his interest in rusty castrating implements.' Her beau would then say, 'I have always had the greatest respect for your father, and of course for you. Let us hold hands and think about the Queen for a while.' If, on the other hand, her father was elsewhere, she would reply, 'The mad old bastard is currently stationed between my sister Constance's thighs. Let us go into the garden and rut like stoats.'
Hence, 'How's your father' became a euphemism for you-know-what."
Provenance: how's your father? catchphrase associated with the British music-hall comedian Harry Tate (1872-1940). Apparently, he would exclaim it as a way of changing the subject and in order to get out of a difficult situation. The phrase either subsequently or simultaneously took on a life of its own meaning the same as a 'thingummy' or anything the speaker did not wish to name. From that, in phrases like 'indulging in a spot of how's-your-father', it became a euphemism for sexual activity.
From _Dictionary of Catchphrases_ (1995) by Nigel Rees