Vicki and Owen Page were happy beyond words when they became parents. Married for five years, and feeling financially stable and settled in their careers, they had been keen to deepen their bond by having children. "We were happy with our lives and felt that having a baby would be the cherry on top of the cake," recalls Vicki.

In the end they got two babies, not one. At 11 minutes past one in the morning on 15 December 2012, Vicki gave birth to one boy and then, 13 minutes later, to another – twin brothers whom the Pages named Olly and Harry. Neither delivery was straightforward. The medical staff at John Radcliffe hospital in Oxford needed forceps to get Olly out, while Harry's arrival in the world involved what his mother remembers as "a lot of pulling and tugging" and uncertainty about what was going on. She assumed that this was due to him being in the breech position – the wrong way up – as he had been for weeks.

"When Harry came out I heard him cry and thought he was fine. I had a huge euphoria moment that I had come through a tough labour and was now the mum of two boys," says 33-year-old Vicki, the HR director of a marketing company. "Owen came over to me, with a massive beam on his face and cradling one of the boys in each arm, and passed them to me. I held them for a couple of minutes before they were put back into the cot." The results of the Apgar tests on the boys' physical condition immediately after their birth seemed to confirm her belief that both her bundles of joy were in good health.

Owen fed and changed the newborns, texted family and friends their big news, then headed home to grab a few hours' sleep. Vicki also tried to get some rest on the postnatal ward, with her sons sleeping beside her in cots.

At 4am she was woken by a commotion and trolleys being moved around. "I heard someone say: 'We need to get a baby ready to go to resus.' My instinct told me it was one of my boys. I thought it was Olly because he was such a small baby, just four pounds and nine ounces when he was born."

In fact, it was Harry whom the nurses took to the resuscitation unit. "I texted Owen to say that he needed to come back to the hospital now because there was something wrong with Harry, though I didn't know what it was. You never in your wildest dreams think it will be something so severe that you end up losing your child, but it was," Vicki says.

Less than 24 hours later, despite being transferred to the neonatal intensive care unit and despite the intervention of an array of experts – neonatologists, cardiologists, paediatric neurosurgeons and neuroradiologists – Harry was dead. Initially baffled by his sudden and dramatic deterioration, the doctors came to realise that he had suffered a massive brain injury while he was being born. They were surprised to find that the obstetrician involved, Dr Ram Mohan, had not mentioned in her notes just how traumatic the birth had been, even though other staff present recalled it as difficult.

That oversight, though, turned out to be merely the start of the doctor's unusual, arguably evasive, response to her actions during the delivery. Mohan's accounts of what she did in trying to get Harry out differed in crucial respects from what two other obstetricians, Dr Alex Cairns and Dr Karin Hellner, and a midwife, Jayne Bruce, who were all present, said had happened, raising questions about her memory or truthfulness.

Her continued insistence that she did nothing wrong – despite extensive evidence to the contrary – amazed colleagues, one of whom described her apparent lack of insight into or contrition for her actions in the operating theatre that night and their catastrophic results as "breathtaking" and damaging to the medical profession.

Her stance is also a source of ongoing trauma for the Pages, who say they will never be able to gain the closure they crave over losing their son unless Mohan finally explains and apologises.

The General Medical Council, which regulates doctors, is investigating Mohan's conduct. Unusually, it is doing so after Professor Stephen Kennedy, one of the country's most senior experts in obstetrics and the Oxford hospital's divisional director for children's and women's services, wrote to it voicing concern about her fitness to practise.

During Harry's birth, his legs, arms and trunk came out straightforwardly. However, his head became stuck. That prompted Mohan to undertake two different manoeuvres which, because of the way she performed one or both of them, caused the injuries that led to Harry dying at 2.03am the day after his birth. Both the Burns-Marshall and Mauriceau Smellie Veit (MSV) procedures are recognised responses to such a situation but have to be done very carefully, without undue force, to avoid damaging the baby. If the doctor applies too much pressure to the base of the baby's skull or top of the neck, that can damage the spine or brain and lead to catastrophic injury.

The Pages say that Mohan performed the MSV once and the Burns-Marshall twice, both "aggressively", and on at least one occasion did it dangerously by taking Harry's body past the vertical position, so that his feet and trunk were moving towards his mother's abdomen, which, the coroner found, is out of line with accepted medical practice. Owen, 49, a warehouse manager for a manufacturing firm, recalls that "she pulled Harry around like a rag doll". Vicki remembers that "the second Burns-Marshall involved force. It felt very unnatural. It didn't feel like my baby should be being put through that. It just didn't feel right. It felt heavy-handed."

Professor Edward Baker, the medical director of Oxford University hospitals NHS trust, which runs the John Radcliffe hospital, wrote to the Pages in March "to offer our apologies for the substandard management of Harry's delivery". The hospital's inquiry had found that "the techniques used at his delivery were not performed safely. It is with great sadness that I recognise that the incorrect use of these procedures led to Harry's death". The trust has settled a lawsuit brought by the Pages on the basis of these failings.

Immediately after the incident, Mohan went on sick leave and was later suspended. She never returned to work in its maternity unit, though soon after was working at nearby Stoke Mandeville hospital in Buckinghamshire.

Darren Salter, the Oxfordshire coroner, in explaining the narrative verdict he recorded after a two-day inquest last November, was clear that the way Mohan performed the manoeuvres caused catastrophic injuries to Harry's brain. He said the MSV manoeuvres caused, among other things, "traumatic haemorrhage" that proved fatal.

As the coroner explained in a letter to the chief executive of the John Radcliffe, which he also copied to the GMC and Stoke Mandeville hospital, where Mohan was then working: "In short, the manoeuvres and force used by the delivering obstetrician caused Harry's neck to be stretched."

Unusually, Mohan's notes about Harry's birth did not mention the Burns-Marshall manoeuvre, though at the inquest she accepted that she used it. She was adamant that she did it only once. However, key parts of her testimony did not tally with that of the three colleagues who were also present at Harry's birth. That prompted the coroner to remark that they had given "important evidence" and that "I can't escape the fact that Dr Mohan's evidence is at odds with others present in the room in some important respects". The report of the hospital's own inquiry highlighted the same discrepancy.

There are unanswered questions about Mohan. Why was she, a senior registrar, given a key role in what was known to be a high-risk delivery, that of twins, one of whom was breech? Why was a consultant not present and in charge? She told the inquest that she had 18 years' experience in obstetrics and gynaecology. Why is someone that experienced, and in her 40s, still classed as a trainee doctor, and not holding a permanent job with any hospital? Health Education Thames Valley, which co-ordinates Mohan's placements in local hospitals, will only say that she is still an obstetrician in training. The Pages are baffled as to how Mohan was the most senior doctor in the room when the second of their twins was born.

Mohan declined to talk to the Guardian or to answer questions about Harry's death, citing her duty of confidentiality, despite the Pages's desperate desire for answers from her. A statement issued through her lawyers at the Medical Defence Union said: "When reporting in detail to the coroner about the matter Ms Ram Mohan expressly asked that her sincere condolences be passed on to Mr and Mrs Page. She would like to repeat those condolences now. Ms Ram Mohan cannot make any further comment at the present time." The Pages recall receiving no such condolences and wonder why she did not take the opportunity of the inquest to say how sorry she felt for them, as others present that night did.

Vicki says that at the inquest Mohan was "cold, calculated and didn't show even a flicker of regret or compassion." She also struck her and Owen as high-handed. They point to Mohan's reply to their counsel, Simon Dyer, asking why her three colleagues said she did two Burns-Marshalls. "I can't speak for them. I did the delivery. I know what happened", she said.

Philippa Luscombe of solicitors Penningtons, the couple's lawyer, says it was "one of the most emotional inquests that I have been to" and added: "I was concerned to learn that Dr Mohan was working in another hospital after her suspension given all of the concerns raised about her, but most of all I was concerned and saddened by the fact that of all of the witnesses at the inquest, she was the one who expressed no emotion or regret at the loss of Harry."

The Pages' lives have been changed for ever. "Every birthday Olly has, everything he does, reminds us that we should be doing it with two boys, not one," says Owen. "Everything from now on will be bittersweet, like Olly's first steps or his first Mother's Day," adds Vicki. "On his first day at school I will be the proudest mum, but also very sad."

Harry's brief life means they have just one precious photograph of their twins, in the brief time they were together on the neonatal ward, taken on an iPhone. "We were robbed of the chance to get a family photo of the four of us together," Vicki said.

• This article was amended on 27 May 2014. An earlier version said Dr Ram Mohan was currently an obstetrician at the Royal Berkshire hospital in Reading. She does not work at the hospital.