The justice secretary, Liz Truss, is to reject making deep cuts in the record 85,000 prison population in England and Wales warning that such “quick fix” solutions would put the public at greater risk.

She is to argue that the biggest driver of the growth in the prison population in the last 20 years has not been longer prison sentences, as is often claimed, but a much tougher approach to sexual offences, domestic violence and child abuse.

The justice secretary is to say that the 140% increase in sex offenders being sent to jail since 2000 and the 75% increase in custodial sentences for violent offenders has led to “a profound change in the nature” of the jail population in England and Wales. Three out of every five offenders are now inside for crimes of sex, drug pushing or violence.

In a speech on Monday to the Centre for Social Justice, Truss will say she wants to see a reduction in the prison population by reforming offenders through early intervention and more effective community penalties, and by better managing those who are locked up.

She will in particular condemn calls by Labour frontbenchers, including most recently from the shadow attorney-general, Shami Chakrabarti, to halve the prison population by handing out shorter prison sentences.

“Reductions by cap or quota, or by sweeping sentence cuts are not a magic bullet, they are a dangerous attempt at a quick fix,” the justice secretary is expected to say.

Her intervention comes in advance of her prisons and courts reform bill which is to be published this month setting out radical reforms to tackle the increasingly volatile and violent situation in prisons in England and Wales. The latest figures record the highest ever level of self-inflicted deaths, assaults and incidents of self-harm across UK prisons.

It also follows a call in November from the previous justice secretary, Michael Gove, for urgent action to reduce prison numbers. He said it was “an inconvenient truth – which I swerved to an extent while in office – that we send too many people to prison. And of those who deserve to be in custody many – but certainly not all – are sent there for too long.”

The last justice secretary to attempt to make serious cuts to the prison population was Ken Clarke, whose proposals for shorter sentences cost him his job in the face of fierce tabloid and political pressure.

Truss is to argue that recent reforms to the criminal justice system have given more victims of domestic violence, rape and sexual abuse the confidence to come forward – and that has been the biggest driver of the growth in prison numbers. The jail population in England and Wales has risen from 40,000 in 1990 to 86,000 in 2012 when it stabilised.

“We all agree it is desirable to have a lower prison population but it has to be for the right reasons,” she is to say. “Public protection is paramount which means managing the prison population in a safe and sustainable way.”

Truss will argue: “It is not the case there has been an upward drift in sentence length across the board. Increases in sentences have only been in particular areas.

“In fact the biggest driver for prison growth in the last twenty years has been the exposure, pursuit and punishment of sexual offences, domestic abuse and other crimes of violence.

“A more understanding and responsive attitude to how we treat victims of sex crimes has seen an increase in reporting and changing attitudes in society that have been reflected in a toughening-up of sentences.”

The justice secretary is to sharply criticise Labour’s Chakrabarti for calling for a halving of the prison population back to the levels of the 1990s saying she did not believe that “the sum of human wickedness” could have doubled in her lifetime.

Truss is to respond saying what actually happened in Chakrabarti’s lifetime was that the police and courts had become far more effective at catching and convicting criminals who have committed the most appalling crimes imaginable, with longer sentences for domestic violence, rape and child abuse.

“It’s not that the sum of human wickedness has doubled – it’s that we have driven that wickedness out from the shadows and put it where it belongs, behind bars,” she intends to say.