Failures made by police in the run-up to the killings of a pregnant mother and her toddler son "more than minimally contributed" to their deaths, an inquest jury has found.

Rachael Slack, 38, and her 23-month-old son Auden were found with multiple stab wounds in their home in the picturesque village of Holbrook, Derbyshire, on June 2, 2010.

They are believed to have been killed by Ms Slack's former partner and Auden's father, 44-year-old Andrew Cairns, who had a history of mental illness.

He was also found dead at Ms Slack's home after turning the knife on himself.

During an inquest at Derby and South Derbyshire Coroner's Court, which began last month, jurors heard that Cairns had been struggling with declining mental health since the break-up of his relationship with Ms Slack in 2009.

Shortly before the deaths he had been detained by police after he had made threats to kill Ms Slack, and was later released on bail.

His mental health had also been assessed by professionals who ruled that he had no major mental health issues and was not a danger to himself or others.

During the inquest jurors heard that Cairns, a former golf tutor who had been prescribed antidepressants, had been known to psychiatric services for a "considerable number of years'' and had been assisted by a variety of mental health services.

Jurors were also told that following his contact with Derbyshire Constabulary, Ms Slack and Auden were deemed as being at high risk of homicide.

Jurors returned verdicts of unlawful killing in respect of Ms Slack and Auden, and found that Cairns took his own life.

As part of their deliberations they were asked by coroner Dr Robert Hunter to consider if it was more likely than not that a failure on the part of Derbyshire Constabulary made a more than minimal contribution to the deaths.

They found that Ms Slack's death was in part more than minimally contributed to by a failure to impress upon her that she was at risk of serious injury or homicide by her ex-partner.

In the case of Auden, jurors found that in part his death was more than minimally contributed to by a failure to impress upon his mother that he was at risk of serious injury or homicide, and a failure to discuss with his mother adequate steps to assess the risk.

The inquest has heard that Cairns was detained by police under the Mental Health Act on May 26, 2010 after Ms Slack drove him to the police station because he refused to get out of her car and she was worried about his behaviour.

He was assessed by mental health workers and released after he was found to have no major mental illness.

The next day Cairns was arrested after threatening to kill Ms Slack but was released on police bail on May 28 after denying the accusations.

The bodies of Ms Slack, Auden, and Cairns were found in the living room of Ms Slack's Victorian cottage on the afternoon of June 2.

Cairns was found dead less than a week after he was bailed by police after being arrested for making the threats to kill Ms Slack.

The inquest heard that Ms Slack told police he had turned up at her house beforehand to play with Auden and said to her: "You are a f****** bitch for abandoning me and getting together with someone else and getting pregnant.

"I've given up everything to be with you. If you are going to make it difficult, I'll make it more so - you've no idea of what I'm capable of. I'll kill you and take him with me.''

As part of his bail conditions he was told not to contact Ms Slack, and a file was also forwarded to Children's Social Care by Derbyshire Constabulary's domestic abuse unit.

Police visited Ms Slack at her home to discuss the incident and security.

The inquest also heard that Cairns visited his doctor clutching a picture of his son just hours before he is believed to have knifed the toddler and his pregnant ex-partner to death.

He visited the Ivy Grove Surgery in Ripley.

Dr Michael Small, who was the duty doctor that day, said Cairns arrived at the surgery in an "agitated and anxious" state, clutching a picture of his son Auden.

Dr Small told the inquest he has assessed Cairns on two previous occasions, on August 23 2009 and March 11 2010. Both times he had been contacted by the Mental Health Team about concerns over Cairns.

Dr Small said Cairns calmed down during the appointment on June 2 and seemed "rational" for the rest of the appointment.

He told the hearing that he had no concerns that Cairns was a risk to himself or others and that the consultation ended on a "positive note".

The inquest had heard previously that Cairns had told Dr Small during the consultation that the next few days were going to be "the most important days of your career".

Dr Small said he believed Cairns was referring to contacting the press about his mental health care.

"He apologised and said it hadn't meant to sound like a threat. It was just important that I took him seriously", Dr Small said.

Dr Hunter said he would be using his powers as coroner to write to the Home Secretary to raise the issues over the powers police have in regards detaining suspects in cases concerning violent or sexual incidents, national training standards in domestic violence for police, electronic document sharing, and mutual disclosure of information.

Professor Steve Trenchard, Chief Executive of Derbyshire Healthcare NHS Foundation Trust, said: "We would like to extend our sympathies to the family and friends of Rachael, Auden and Andrew for their loss of a loved one in this tragedy.

"We welcome the Coroner's findings that there was no evidence presented over the past six weeks regarding Andrew's care that a jury could properly consider was in breach of Article Two of the European Convention of Human Rights.

"We will assess the jury's conclusions and Coroner's comments in more detail as part of our determination to be always changing, always improving, to meet the needs of the people of Derbyshire we serve.

"Immediately after this incident in 2010, we launched our own investigation into the full circumstances behind it.

"We developed and delivered a far-reaching action plan to improve the quality of our care and take it to new levels of best practice wherever possible."

Assistant Chief Constable Karl Smethem, from Derbyshire Constabulary, said: "On behalf of Derbyshire Constabulary I would like to express my deepest sympathy to the family of Rachael and Auden Slack. They have faced with great dignity the horror of what happened to Rachael and Auden in 2010.

"Rachael and Auden died in their home, at the hands of Andrew Cairns, her former partner and Auden's father. Rachael was a very kind and caring person who had been concerned about Andrew Cairns' mental health and had done all she could to get him help and to support him.

"Since Rachael and Auden's deaths, two reviews have been conducted.

"We asked the Independent Police Complaints Commission to consider the contact we had with Rachael prior to her death. Additionally, we have contributed to a Serious Case Review which has looked at the actions of all the agencies which were involved in this case, including the Derbyshire mental health services and social services. This was carried out by an independent author and the review will be released within the next few weeks.

"I am confident that Derbyshire Constabulary's policies and procedures for the investigation of domestic violence incidents, and for the protection of victims, met national guidelines in 2010.

"F rom the evidence it is clear that Rachael's report of Andrew Cairns' verbal threat to kill was taken very seriously by the police. We were actively investigating the threat, with a view to charging him, and we did take steps to ensure that Rachael and Auden's home was secure.

"As a result of the two reviews which have taken place and subsequent advancements in national guidelines, we have already developed and improved our domestic violence policies and procedures. However we will now review the evidence heard at the inquest, and the jury's findings, to see if any further changes are necessary to ensure that the service we provide to the public of Derbyshire is as good as it can be."