The former cabinet minister Chris Huhne has described prison as a "humbling and sobering experience" as he and his ex-wife Vicky Pryce were released on Monday, returning to their London homes to contemplate how to rebuild their shattered reputations.

Both had served 62 days of eight-month sentences for perverting the course of justice after Huhne, 58, asked Pryce, 60, to take three speeding points for him a decade ago. They were freed under home-detention curfew and must each wear an electronic tag.

Later, outside the north London home he shares with PR adviser Carina Trimingham, 46, for whom he left Pryce, the former energy secretary apologised for what he had done.

As Pryce arrived at the former family home in Clapham, she posed for photographs briefly while her lawyer said his client was very pleased to be home and looked forward to returning to her career as an economist.

Within hours of Pryce's release, it was announced she would publish a book called Prisonomics in September. Iain Dale of Biteback Publishing, the Greekonomics publisher, said it would be a personal account of prison life combined with an economic analysis of the cost to the economy of keeping women in prison.

In a statement through Biteback, Pryce said: "I kept a diary while in prison and I have some strong views on how the prison system works, especially with regard to how it treats women. I will use personal experience to back up my arguments but I must be clear that this book is more than a memoir – it will analyse how prison works, and should work very much from an economic perspective."

Pryce, a mother-of-five, with three of the children with Huhne, appears determined to resume her high-flying career. The former joint head of the Government Economic Service resigned as senior managing director at FTI Consulting after being convicted of perverting the course of justice after a retrial in March. She had unsuccessfully put forward a defence of marital coercion.

It emerged that her most recent work, Greekonomics, about Greece's struggle with debt and the euro crisis, had been considered a possible contender for the prestigious Orwell prize, but was dropped because of her conviction.

Huhne, a former City analyst, is said to be looking forward to starting a fourth career, with frontline politics no longer an option. His appointment to the Department of Energy and Climate Change is understood to have kindled a genuine passion in renewable energy and he may seek to explore options in that field.

Shortly before he changed his plea to guilty at the start of his trial in February, Huhne was appointed as a consultant to the green energy company Nationwide Energy Services, a fast-growing firm that helps people obtain grants to make their homes more environmentally friendly. A publishing deal may also be possible, especially if the former journalist, who was elected as Liberal Democrat MP for Eastleigh, Hampshire, in 2005, kept diaries during his time at the heart of the coalition government.

It is understood he has considered writing about prisons and prisoners' lives, with all proceeds going to charity. He has also, reportedly, expressed an interest in the rehabilitation, re-employment and aftercare of prisoners.

Another option for Huhne, who gained a starred PPE first at Oxford University, may be to reinvent himself as a lecturer, possibly abroad, where he will be out of the spotlight.

Huhne left Leyhill prison in Gloucestershire by the main entrance in the back seat of a silver Honda at about 7.30am, making no attempt to avoid waiting media.

After arriving at his home in Clerkenwell, with Trimingham at his side, he said: "I would just like to say once again, as you know from the night I was sentenced, I said that I was very sorry for what I had done. It has been a humbling and sobering experience. I would like to thank all of those who have written to me – hundreds of letters that I have had – and all my family and friends who stood by me. And I would also just remind you that I have served only part of my sentence and therefore it is not appropriate to say more.

"I would now like to get on, get back to home, and continue with my life. Thank you for coming."

Pryce left East Sutton Park prison near Maidstone, Kent, through a back entrance, driving away with her solicitor, Robert Brown, and pursued by press photographers outside the Category D open jail for women and young offenders.

Arriving at her south-west London home, smiling, she told reporters the first thing she planned to do was have a cup of coffee. Her solicitor said: "Vicky Pryce is very pleased to be home and back with her family. She is grateful for all the support she has received from everyone whilst in prison, including her fellow residents and prison staff.

"She now intends to spend time with her family and looks forward to returning to her career as an economist."

During her trial, Southwark crown court in south London heard Pryce had revealed the speeding points scandal to a newspaper in 2011 in an attempt to "nail" her former husband after he left her for Trimingham.

The Crown Prosecution Service seeks more than £100,000 in costs from the former MP. Last month a hearing was told that Huhne's legal team had offered £25,000. The CPS seeks £48,695 from Pryce, the court heard.