That’s it then. Sir Edward Heath was a paedophile. It has been on the news for four days, so it must be true. They might just be allegations, but we know there is “no smoke without fire”. The chap was a “confirmed bachelor”, nudge, nudge. They are always a bit fishy, these lonely sorts.

I suppose many people just shrug and say public figures must take the rough with the smooth, even when they are dead and defenceless. But the current police obsession with “historical celebrity sex abuse” is beyond bizarre. By any standard, it risks rampant injustice.

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The Heath story is underpinned not by what used to be called “evidence”, but by a deluge of vague and anonymous “claims”. Each day another police force climbs on to the bandwagon by following allegations said to be “pouring in”. They are never enumerated, dated or specified.

As far as Heath is concerned, there appear to be only two firm allegations. One comes from a man who says he was raped by Heath in 1961 in a flat in Park Lane full of sailing paraphernalia. (Heath had no such flat and was not a sailor then, according to his biographer, John Campbell.) The Daily Mirror printed an immaculately written letter from the unnamed man, now in his 60s. The Metropolitan police investigated it some weeks ago and said it offered “no lines of inquiry that could proportionately be followed up”. That seems a not unreasonable response.

The other is from an anonymous former policeman in Wiltshire who alleged that a Myra Forde had, in the mid-1990s, threatened to expose Heath as a paedophile if she was prosecuted for running a brothel. She denied the whole story on Wednesday, which perhaps explains why Wiltshire’s police and prosecutor say they were never told of the threat, although they nevertheless held a press conference outside Heath’s former home in Salisbury last weekend.

Even before the woman’s denial, this seemed a very thin basis on which to destroy a man’s reputation. Yet the gutter has been dredged. Care homes in Jersey and Northern Ireland are said to be investigating “claims” of Heath making yachting visits to abscond with children. Police operations with fancy names such as Midland and Whistle embrace Heath. One has to wonder if it is not to validate what has become a booming cottage industry.

I was one of many political journalists entertained by Heath after his fall. Gatherings in Salisbury and at party conferences were intriguing rather than jovial. Few women were present. Our assumption was that Heath was gay, though with no evidence. Nor was there any rumour of his association with the known Dolphin Square set and the late Sir Peter Morrison. Had there been, the gossip would have been electric. The topic of Heath’s sex life consumes four pages of Campbell’s excellent biography of the man, drawing a plausible blank.

Those close to Heath have expressed dismay and astonishment at the latest witch-hunt

Those close to Heath have expressed dismay and astonishment at the latest witch-hunt. Lorrie Eathorne-Gibbons, his local agent, and his close aide, Brian Binley, flatly disbelieve the claims. Out of curiosity, I did once ask his then closest female friend, Rosemary Wolff, about his private life. She simply said, “He has none.” Campbell even rejects the story of the bedside picture of his friend, Kay Raven.

Nothing should detract from the awfulness of child sex abuse, and the impact it can have on its victims. Accusers can always be accused of fantasy or malice. But the case against Heath rests on two allegations from questionable sources, unsupported by any evidence of his sexual proclivities over 60 years of adult life, for most of which he was monitored around the clock by police close protection. They strike me as plain implausible.

However loud the mob may howl, there is no sight of a fox. Historical sex abuse is currently the nation’s favoured blood sport. Most countries apply a 10-year statute of limitation to such crimes. In Britain, the field is open indefinitely to the living and the dead. Police and BBC websites openly invite the public to name any celebrity they think might once have molested them. They will enjoy secrecy and possible compensation.

Cliff Richard remains in limbo following a highly publicised police raid last summer on his Berkshire home when he was on holiday. No attempt was made to inform him or reach him about what turned out to be a 30-year-old allegation, but the BBC was allowed to film it from a helicopter. The raid was described by barrister Geoffrey Robertson as “a deliberate act of defamation”.

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Police and prisons are overwhelmed by the Home Office’s obsession with sex offences. An extra 650 offenders have been jailed in the past year alone. The dead may be safe from prosecution, but not from defamation. They are at the mercy not of the law, but of history. But police and media still have some obligation to fairness and proportionality.

The past week’s assault on Heath’s reputation has clearly been driven by defensiveness over Jimmy Savile and by past police neglect of sex abuse cases. It has been driven by political antipathy to Heath, by latent homophobia and by a general suspicion of people who seem to lead abnormal lives.

Perhaps one day some irrefutable fact against Heath does emerge. Perhaps the Goddard inquiry into establishment sex crimes will make an astonishing revelation. For the time being, night after night, a clear injustice is committed. It is sick.