The public's collective memory doesn't operate in political cycles. They remember when burnt-out cars were ubiquitous, when communities were terrorised during, before and after bonfire night by the misuse of fireworks. Londoners remember the rough sleepers on our stations and shop doorways, and everyone remembers that crimes were too many and police officers too few.

Antisocial behaviour was described as low-level nuisance. The police and local authorities had few powers and no combined structures to deal with it. The police didn't even have the power to take truants back to school.

This was the country we inherited in 1997. We didn't solve every problem and, as I stated last year, there was a period when we put antisocial behaviour on cruise control because of other priorities following the 7 July London attacks, but we did an enormous amount to tackle crime and antisocial behaviour, and any but the most ungracious and mean-spirited government would recognise that.

Cue the home secretary's speech this week on asbos. She set out the scourge of antisocial behaviour exactly as I would. She even nicked my mantra – ASB needs to be tackled not tolerated. But she went on to give the most bizarre and distorted picture of what's happened over the last 13 years.

Let's get the myths out of the way first. We introduced a range of civil powers for the police, local authorities and other agencies to use in a co-ordinated way to tackle the kind of behaviour that, while falling short of criminality, destroys people's lives.

They were not driven from Whitehall, as May suggests, but were pursued through the crime and disorder reduction partnerships established locally, involving community groups and social enterprises as well as the police and local authorities.

Very often, where the ASB is caused by someone under 18, a letter or visit to the parents by the police solves the problem.

Where more co-ordinated action is necessary, parenting orders and acceptable behaviour contracts (ABCs) have proved their worth. Family intervention projects ensure that all aspects of a dysfunctional family's behaviour are addressed in two years of intense support and intervention.

An asbo is the most serious civil power. Lasting for a minimum of two years, it sets out a list of conditions, the breach of which is a criminal offence, with a maximum of five years' imprisonment.

Yes, they are breached. Unsurprising given the previous behaviour of those who are on them, but the success rate is good and the problem of breaching needs to be addressed through driving up the low level of prosecutions when this happens, not by abandoning asbos.

Theresa May said that for 13 years people had been told "that the asbo was the silver bullet that would cure society's ills". Who said that? When?

What the National Audit Office and the Audit Commission actually said is that our approach to ASB worked, with 65% of the NAO's review sample desisting after the first intervention and 93% after the third.

More needs to be done, particularly in speeding up the process and empowering citizens to take out legal injunctions. But the most surprising thing about May's speech, in among all the platitudes, was the failure to acknowledge any success at all. Indeed, she resorts to disingenuousness when she says that ASB has become more frequent.

On 15 July her department published the statistics. It said: "The current proportion of people who had a high level of perceived ASB is the lowest since the measure was introduced in the survey in 2001/2 … In previous years reduction [with problems with abandoned or burnt-out cars] was largely responsible for driving falls in the composite measure. However, the reduction in the overall measure of ASB between 2008/09 and 2009/10 reflects falls in the proportion of people perceiving a problem with almost all strands of ASB."

Getting rid of asbos would be entirely consistent with the usual Tory approach to crime and disorder. It's called laissez-faire and it will soon be reflected in the other thing that comes with Tory governments – it's called rising crime.