David Gauke has used what is likely to be his valedictory speech as a cabinet minister to urge his successor to scrap short prison sentences.

The justice secretary, speaking in London, said new government research showed that about two-thirds of offenders on prison terms of less than 12 months would reoffend, compared with a third of those given a court order. He said the findings had reinforced his view that moving away from terms of up to six months would deliver change.

He said this could be done by introducing a bar to prevent the courts using short sentences or at least a presumption against using them – as had been done in Scotland for terms of up to 12 months.

Gauke, along with the chancellor, Philip Hammond, is among a group of senior Tories strongly opposed to a no-deal Brexit, nicknamed the “Gaukward squad”.

Gauke, who has also spoken out against the poisonous impact of populist politicians in Britain, is expected to be removed from cabinet after 18 months heading the Ministry of Justice after the likely election of Boris Johnson as Tory leader and prime minister next week.

Alluding to his expected departure, Gauke said: “I believe that the approach that I’ve set out today – indeed, the approach I have set out in the last 18 months – is one that is most likely to be effective in reducing reoffending and therefore reducing crime.

“I am aware that it is an approach that will not have universal support but I have taken great encouragement from the widespread support for an evidence-led, rehabilitative and humane agenda.

“It is my hope that in the years ahead – whoever has the privilege of being justice secretary – it is an approach that will be pursued with persistence and determination and courage. And that will help deliver a safer and more civilised society.”

The MoJ research, published on Thursday, shows the estimated cost of reoffending is more than £18.1bn a year in England and Wales, which covers the costs to victims, police and wider public services.

The data shows that 64% of offenders released from custody between April and June 2017 after a short custodial sentence of less than 12 months reoffended within a year – almost double the 34% rate for those on a court order, such as a community sentence or suspended prison term.

More than two-thirds – 68% – of those in prison for six months or less have a drug-use problem, while 60% do not have a stable or suitable place to live, according to the new research. Compared with offenders serving community sentences, the proportion of those facing these problems is reduced to 33% and 31% respectively.

Christina Marriott, chief executive of the charity Revolving Doors Agency, said: “Revolving Doors’ campaign, Short-sighted, has made the robust case that short prison sentences drive reoffending, create more crimes and more victims. We have a once-in-a-decade opportunity to save lives and reduce crime. The new prime minister should urgently back a consultation on this important policy.

“We have proven the consensus for a new positive approach; 70% of MPs back restricting short prison sentences and the majority of the public want people with drug and alcohol addictions to get treatment, not prison, where possible.

“That eight out of 10 people sent for a short spell in prison for theft are reconvicted within a year is a shocking rate of failure. Revolving Doors’ campaign has shown that we can do better. Restricting the use of short jail terms is a smarter approach that could make our justice system more effective, reduce crime and save lives.”