The allegations about what went on at Westminster in the 1980s demand a rigorous investigation

As with the inquiries into phone hacking, Jimmy Savile and Hillsborough, there is nothing to lose, and everything to gain, from a similarly rigorous approach to the allegations of historical child abuse in politics – in Westminster and in local government.

A high-profile, open, independent investigation would embolden victims to come forward, prompt witnesses to approach the authorities, and pressure those at fault to admit wrongdoing. Evidence should be given under oath; the danger of perjury would concentrate the minds of all concerned. The Home Secretary fell short of at least some of those objectives when she outlined the Independent Panel and other reviews to the Commons yesterday. These are only the first steps in the right direction, confined as they are to documents and officialdom, and hers was a curiously bloodless performance given the cruelty to vulnerable children by the powerful that may have taken place. In any event, sooner or later we will need to go much further.

The victims deserve justice, and it must not be further delayed. This is unlikely to be a tale of one organised conspiracy, a giant gang with all the perpetrators acting in concert over decades. It is likely to be a series of different scandals, some linked, as with some of the showbiz cases. The new inquiry must hunt for any linkages between local authority children’s homes and the procurement of children for abuse.

If some of these areas become a matter for the police, the authorities must press them to spend the money needed to secure convictions, as with the hacking cases. It will not be straightforward; with the passage of time, some victims will be dead or unable to testify – damaged children turning into damaged adults with the usual mix of emotional problems and drink and drug abuse.

Some will have partial memories; taken together, however, their testimonies may illuminate some very dark recesses. It may be that those testimonies already exist among the documents that the Home Office and police did manage to retain. The inquiries will surely make these their priority.

The inquiries announced by Theresa May will not, by contrast, clear the names of those named in lurid web conspiracy theories. And those cited in the wilder reaches of the internet should have their reputations restored by an open and transparent process. Unhappily, this will not take place soon.

Wherever there is a ring, or rings, of the sort being suggested there is the opportunity for blackmail, and it is implausible to imagine that those who may have procured children for abuse – from local authority homes or elsewhere – will have done so without some thought to the advantage this may bring them with powerful individuals, maybe in local and in national politics. Untangling such connections will take even greater time and resources, but is another essential line of inquiry.

We are becoming used to being shocked. Over a few decades almost every pillar of British society has been found wanting. The Guildford Four, Birmingham Six, Stephen Lawrence and Hillsborough affairs exposed gross police malpractice; the Leveson inquiry did the same for the press; cash-for-questions and MPs’ expenses shredded the political class; the Iraqi supergun and Hutton inquiries revealed the compromised state of our security services; the Savile and related inquiries shamed the BBC, show business and the NHS; the City, the Catholic Church and various branches of sport have also been shown to be corrupt. Yet those discoveries in fact are the affirmation of a healthy, vibrant democracy; and a step to repair and a renewal of trust. Ms May has taken only a first, small step along what may prove a harrowingly long road to the truth.