Sitting in the kitchen of Vicky Pryce's elegant south London home, it's hard not to think about the differences between her life and the lives of most of the women she met as she was serving her prison sentence earlier this year. Released from East Sutton Park open prison in May on an electronic tag after serving eight weeks of her eight-month sentence, Pryce has published a book about her experience. A combination of diary and economic analysis of the prison system, entitled Prisonomics, it is a sobering, compelling read that would serve as a blueprint for any politician who wanted to focus seriously on reform.

Pryce understood immediately how lucky she was to have been able to make provision for her family before she received her sentence, leaving cheques, she writes, "for the pest control man, the milkman and generally for ensuring that the house and my children who lived there would survive my absence, at least financially".

As she points out in the opening chapter, 15% of prisoners report being homeless before entering prison. Many more faced eviction because of rent arrears. Significant numbers of children whose mothers go to prison end up in local authority care and the rest are looked after by family, friends or acquaintances. Reseach suggests that more than half of women who go to court are not expecting a custodial sentence – children are often left with neighbours and mothers are often reluctant to notify social services in case the children are taken away and the family is further disrupted. About 17,000 children a year are separated from their mothers by imprisonment and figures show that adult children of imprisoned mothers are more likely to be convicted of a crime than adult children of imprisoned fathers.

Pryce, a mother of five, doesn't want to talk about her family or her ex-husband, former cabinet minister Chris Huhne, whose motoring penalty points she took 10 years ago, leading to them both being imprisoned. Neither would I want her to – I am interested in what she made of prison. Did she feel that what she had done was so bad that she deserved to be locked up? "I didn't even think about that," she says. "The sentence was what society, in the form of the judge, had decided was necessary and I knew I had to do it. The important thing was to come out of it strong for my family and able to do something worthwhile."

Has it made her a better person? "I'd hate to think you have to go to prison to be a better person," she says. "I would not recommend anyone going to prison, but I think I would have been much less of a complete person if this hadn't happened. There would have been a whole chunk of something very important that is happening in society that I would not have realised was going on."

Pryce came to Britain from her native Greece alone as a teenager and worked in hotel room service to pay for O- and A-level studies before gaining a scholarship to study at the LSE. Her career as an economist took her to the highest levels of government. In 2002 she became the first woman chief economic adviser at the Department of Trade and Industry and in 2007 became joint head of the government's economic service. When the news broke that she had been sent to prison, I felt, like many, that the sentence was a disproportionate response to the crime – perverting the course of justice. But Pryce has worked with charities that help unemployed people and ex-offenders so it may be no bad thing for a respected expert in economics to have a look at what is going on in our prison system from the inside.

Having worked in undeveloped countries in dangerous and unpredictable environments, Pryce says she felt no fear about going to prison. "Holloway was a great big chaotic place, but as soon as I started speaking to other girls it was very clear to me that prison was not necessarily the best thing for them. So many had problems that were not being dealt with and wouldn't be dealt with in prison. There were many who were in for things that you would have thought society could have dealt with in a different and more helpful way. So straightaway I was thinking about these things. You see what goes on in Holloway and you wonder what is gained for society by keeping people in those conditions. I began writing and making loads of points. There was no internet, so I had to wait till I got out to do proper research. People would send me stuff, like the Corston Report on women in prison and economic stuff. It was quite obvious that this needed to be looked at from an economic viewpoint."

Her observations brought logical conclusions. "The majority of women, over 80%, are in prison on short sentences of less than 12 months for non-violent offences. A good proportion of these women are mothers. The annual cost per prison place for a woman is more than £56,000, yet intensive community orders cost less than a third of that and evidence shows they have more impact on reducing reoffending. It makes no economic sense to keep women in prison who present no threat of harm to others. Prison often exacerbates the problems these women were facing before they were sent away. The lack of co-ordinated governmental thinking on this is perpetuating the problems and doing nothing to lower costs or re-offending, which costs a staggering £9bn or £10bn a year."

Her grasp of the facts is startling. But how are politicians and decision-makers to be persuaded that changes are necessary and beneficial? There was bad news for the justice secretary Chris Grayling this month when Nick Hardwick, the chief inspector of prisons, published his annual report. Since he took over from Ken Clarke in September 2012, Grayling has been trumpeting his Transforming Rehabilitation agenda yet has presided over an increase in prisoner numbers of more than 3,000 in England and Wales. Hardwick reports that too many prisoners are spending too long locked in their cells with nothing constructive to do. He says that the quality and quantity of "purposeful activity" in prison has "plummeted" in the past 12 months and describes his findings on Grayling's watch as "the worst outcome for six years".

How would Pryce advise Grayling? "If there is a rightwing agenda, it's very hard just to change the language," she says. "What he needs to do is think very seriously about whether the present system works, which it clearly does not, and whether it gives value for money, which clearly it doesn't do either. The current approach is simply going to lead to your resources being spread too thinly and the benefits to society just not coming. If we just keep locking people up for longer and longer then all that happens is that recidivism is going to keep increasing. The cost to society then is going to be far greater than it needs to be. I think if anyone was to explain it in those terms, the savings for the taxpayer, fewer potential victims, this I think would be a vote winner. But it might just be a bit too complicated for him."

Pryce has often been depicted in the press as hard and manipulative. But when she speaks there is a quiet dignity in her voice and a strength I hadn't quite expected. Next month she takes up a visiting professorship at Warwick University and demand for her professional expertise in the City is high. After all she has been through I wondered why she still cared about prisons. Why not just put it behind her and get on with rebuilding her career? "Well you can't just ignore it when you have an experience in life like this. Being an economist I couldn't just bypass what I saw as a lack of economic rationale in what I found in prison. More important are the stories of the women and what happens to the children and the repercussions for society as a whole that has a huge impact and we are just not told. Few women in prison have a voice and I do have a voice and I want to use it to inform a serious debate. If what I have done with this book encourages a wider debate then at least I will have done something right for the girls I met and hopefully for whoever else is out there who may be heading that way."

Later that evening I attended a conference in London, organised by Re-Unite, the charity that helps keep mothers in prison connected to their children, where Pryce was due to speak. It was her first contribution to such an event since her release from prison. The hall was packed with representatives from penal reform and female prisoners' charities. Potentially this was her toughest audience. As she stood up and scanned the rows of expectant faces, she looked fragile and vulnerable – until she started talking. Eloquent and confident, she spoke without notes and without rancour. The applause when she sat down was testament to her credibility as a new and powerful force in the prison reform debate.