The general view, and Ken Livingstone's, seems to be that the revelation (not that it was ever a secret) that he has five children with three women will not damage his chances in the election for Mayor of London.
It may even improve them, if we are still influenced by Victorian values: there is a story about Disraeli's principal political opponent, the septuagenarian Lord Palmerston, being caught in flagrante delicto with a chambermaid on a billiards table in a stately home in Suffolk. One of Disraeli's advisers then suggested that the story be spread around, to which the great man replied: "Good heavens, no! If this gets out, he will sweep the country!".
The same anecdote, which may well be apocryphal, sometimes crops up with Gladstone substituted for Palmerston. That version seems unlikely, as it is generally accepted that Gladstone was a man of the utmost probity: allegations that his work in founding the Church Penitentiary Association for the Reclamation of Fallen Women and arranging employment for ex-prostitutes was not inspired entirely by altruism were investigated in a court case after his death, and the jury unanimously found that the evidence "completely vindicated the high moral character of the late Mr W.E. Gladstone."
It may be that the allegations were made by those who had been outraged by Gladstone's attacks on the Roman Catholic Church, which in pamphlets he had described as "an Asian monarchy: nothing but one giddy height of despotism, and one dead level of religious subservience". He also commented that Church's Decree of Papal Infallibility had placed British Catholics in a dilemma over their loyalty to the Crown and their loyalty to the Pope, urged British Catholics to reject papal infallibility as they had opposed the Spanish Armada of 1588, and asserted that the Pope wanted to destroy the rule of law, replace it with arbitrary tyranny, and then to "hide these crimes against liberty beneath a suffocating cloud of incense". These remarks have a resonance today in the current dispute over the Embryology Bill.
This was strong stuff. It is hard to imagine a modern prime minister disparaging even a minority faith in such a way: it would lose more votes than any amount of alleged hanky-panky on billiard tables.