Here is Stephen Hawking’s verdict on the movie about his marriage: it needed more science. And here is Jane Hawking’s verdict: it needed more emotion. Those opposing views on The Theory of Everything, which brought Eddie Redmayne an Oscar and a Bafta for his portrayal of Stephen and Felicity Jones Oscar and Bafta nominations for her portrayal of Jane, reveal a great deal about not only the personalities of the world’s most famous scientist and his former wife, but also one of the major strands of difference in their relationship.

But the truth is that science is probably more absent from the film than emotion, because what the film represents is a triumph of Jane’s experience and persona after decades in which the family was viewed solely through the prism of Stephen’s genius, who as well as being the world’s best-known scientist is also the world’s best-known sufferer of motor neurone disease (MND).

Today there is an aura of unassuming achievement around Jane, who is sitting in the conservatory overlooking her garden in a quiet corner of Cambridge. Meeting her feels like fast-forwarding through time to meet an older Felicity Jones, so accurately did the actor represent her subject. But then, talking to Jane, it all turns on itself again: the reality was, she says, that she and Stephen met Jones and Redmayne when they were researching their roles, and was later astounded to realise how closely her mannerisms, gestures and speech patterns had been noted. “When I saw the film, I thought: she’s stolen my personality!”

Her relationship with Stephen started when both refused to be daunted by the fact that Stephen had just been diagnosed with terminal motor neurone disease. They ploughed into marriage in the face of his parents’ pessimism about its chances of success, and had three children. In the face of pressures that were almost too much to bear, and alongside her friendship with another man, they somehow kept their marriage together for a quarter of a century before ending it with a remarkable degree of equanimity.

Does the film present an accurate portrait of their marriage, which began at Trinity Hall in Cambridge in 1965?

“The important thing is that the feelings, where they are there, are very much true to our experiences. So from an emotional point of view, it’s spot on. The only thing is that they’ve had to minimise the strains and struggles, because in our real life the difficulties of dealing with Stephen’s disease were much greater than they appear in the film.”

And, yes, the impression given in the film that she and Stephen managed to split up without too much acrimony – and that Jane’s new partner and now husband, musician Jonathan Hellyer Jones, became part of their immediate family – is indeed an accurate one (although for a long time after they met, their relationship was platonic).

Jane met Jonathan when, to give her a break from the constant demands of caring for Stephen, a friend suggested she should take up singing in the local church choir, run by Jonathan. It was 1977. The Hawkings, then parents of two young children, were living in Cambridge, where he was garnering a reputation as one of the most glittering scientists of his generation. Jane, though, was isolated and overwrought. How much were the demands on their marriage the product of Stephen’s disease – without it, might they still be married today? Jane isn’t sure: although his health was a huge strain, there were others. From the outset, Stephen’s “eccentric” family made no secret of the fact that they didn’t think the marriage would survive.

“Stephen’s mother once said to me, ‘We don’t like you because you don’t fit into our family.’” On another occasion she learned by chance that the Hawkings were planning to move to Cambridge so they could be there when the marriage foundered, as they were sure it eventually would.

But it wasn’t just about a lack of support from the wider family. “The truth was, there were four partners in our marriage,” says Jane. “Stephen and me, motor neurone disease and physics. If you took out motor neurone disease, you are still left with physics. Mrs Einstein, you know, cited physics as a difference for her divorce ...”

During their marriage, she says, Stephen would retreat into himself. And, though he tried to explain physics to her, she always felt shut out of the world that was so crucial to him. But the stresses of MND were not solely or even mostly down to the physical difficulties of the condition; what brought even greater disruption to their lives was the advent of the carers who shared their home, who disapproved of aspects of their lives, and whose presence meant they could never have the privacy that every family needs to thrive.

“They whispered about us and they undermined me,” says Jane. It’s clear the pain is still there. One of those nurses, Elaine Mason, went on to become his second wife, though the two later divorced. This is an episode of their lives Jane is reluctant to rake over, although it was this relationship that tipped the Hawkings into splitting up, rather than her relationship with Jonathan. Why did they carry on for so long, even after she had met Jonathan and become close to him? She says it never felt like a choice: she loved Jonathan and depended on him for support, but she absolutely loved Stephen as well.

“There was no alternative to just carrying on. I felt very committed to Stephen, and I didn’t think he could manage without me. I wanted him to carry on doing his amazing work, and I wanted the children to have a stable family behind them – so we just carried on.”

In real life, as in the film, Jonathan became part of the family, sharing the workload of caring for Stephen with Jane, and helping bring up the children. He had been widowed a couple of years before they met. “What brought us together,” says Jane, “was loneliness. We were both very lonely people, and then we found one another.”

So the formal split in the Hawkings’ marriage didn’t come until the early 1990s, by which time the oldest children were in their late teens and 20s and the youngest late addition, Timothy, was 10. In real life, as in the film, Jane says there is no doubt that Timothy is Stephen’s child, not Jonathan’s. She is proud of the way she and Stephen and Jonathan kept their lives on an even track for so long. “But once the breakup happened, things absolutely exploded. The lines of communication became much more difficult for a while.”

Even when a marriage has petered out gradually, it still takes time to recover, she says. “They reckon you have to allow at least one year for every five years of marriage to recover before you can pick up the reins and find yourself again.”

Jane and Jonathan eventually married in 1997. How has that union compared with her first one? “I don’t think of my life as having two marriages, I think of it as a continuum,” she says. “We all lived in such harmony, and for so long, until the divorce and the disruption.”

But her two relationships have been very different. “I’ve been able to lean on Jonathan – we can lean on one another,” she says.

“Whereas in the past with Stephen, he was dependent on me all the time. He worked very hard and he was very successful, but I never felt I could lean on him emotionally or confide in him.”

Another difference is that, where physics divided her and Stephen because she was not of that world, music unites her and Jonathan: he is head of music at Magdalene College, and Jane sings regularly in choirs and as a soloist.

Today, Stephen lives just round the corner from Jane and Jonathan. When we meet, she has just returned from visiting him, and they’re all planning to meet for Sunday lunch with Lucy, the couple’s daughter, at the weekend.

Stephen has taken part in many of the publicity events for The Theory of Everything, which was based on Jane’s memoir of their time together. Now 71, she and Jonathan divide their life between Cambridge and their house in northern France, and she makes regular visits to Seattle where her and Stephen’s eldest child, Robert, works for Microsoft and has a son and a daughter.

Lucy is the mother of an autistic son, so as a grandmother Jane has taken up the cudgels she once employed as a wife, and campaigns for better rights for disabled people – her current battle centres on the cuts to the Independent Living Fund, which she says will stop people like her grandson from living independent lives. It has brought her full circle, and she feels as passionately about it as she ever did.

“Being Stephen’s carer was such a struggle, and it’s a lonely job looking after a disabled person. Thinking back, I honestly wonder how I got through it. But what you hope is that the years since have brought improvements to the lives of disabled people and their carers, and I think for a while it was like that. But now the clock is turning back, and we can’t let that happen.”

• The Theory of Everything is out on DVD