The families of the victims of the Nottingham attacks have said they “face their own life sentence” of ensuring Valdo Calocane “is never released” after the Court of Appeal ruled his sentence was not “unduly lenient”.

The relatives of Barnaby Webber, Grace O’Malley-Kumar and Ian Coates reiterated their calls for a public inquiry into the attacks in Nottingham last June, with the mother of Mr Webber claiming that Calocane should become “the next Ian Brady and Fred West” by never being released from custody.

Three senior judges ruled on Tuesday that Calocane’s indefinite hospital order was “not arguably unduly lenient”, stating the court could not ignore medical evidence related to Calocane’s paranoid schizophrenia.

The Attorney General referred the sentence to the Court of Appeal in February, with lawyers arguing that Calocane, 32, should have been given a “hybrid” order, where he would be treated in hospital before serving the remainder of the sentence in custody.

Speaking following the ruling, Mr Webber’s mother, Emma Webber, said: “Today’s ruling comes as no surprise to the families of the Nottingham attack victims. It was inevitable and was not a review of anything other than the letter of the law as it stands.

“Despite the fact that the Attorney General herself feels that Valdo Calocane did not receive the appropriate sentence, today’s outcome proves how utterly flawed and under-resourced the criminal justice system in the UK is. It also illustrates the need for urgent reforms in the UK homicide law.

“The fact remains, despite the words of the judge, that almost 90% of people serving hospital orders are out within 10 years and 98% within 20 years. In effect, the families now face their own life sentence of ensuring the monster that is Valdo Calocane becomes the next Ian Brady or Fred West and is never released.

“Given the failed investigation carried out by Nottingham Police, the weak prosecution put forward by East Midlands CPS and the over-reliance on doctors’ reports, there was probably no other conclusion that could be made.”

She continued: “There are many, many more serious questions that the families will now continue to fight to get answered.

“We do not and never will agree that the vicious, calculated and planned attacks carried out were that of an individual who was at zero level of capability.

“We have never disputed that he is mentally unwell; however, he knew what he was doing, he knew that it was wrong; but he did it anyway. There should be an element of punishment for such a heinous act; alongside appropriate treatment.

“This is just one part of the fight for justice and appropriate accountability for failures that the families have been forced to endure. So far, there have been no less than eight individual reports, reviews and investigations.

“We do not believe that there is any chance these can be cohesive enough to ensure a full and detailed outcome, and therefore call for a public inquiry.”

Calocane fatally stabbed 19-year-old university students Mr Webber and Ms O’Malley-Kumar as they walked home from a night-out in the early hours of June 13 last year, before killing 65-year-old Mr Coates and stealing his van.

He then used the vehicle to knock down three pedestrians – Wayne Birkett, Marcin Gawronski and Sharon Miller – in Nottingham city centre before being arrested.

Prosecutors accepted his not guilty pleas to murder at his sentencing at Nottingham Crown Court in January after multiple medical experts concluded he had paranoid schizophrenia.

Sentencing judge Mr Justice Turner told Calocane that his “sickening crimes” meant he would be detained indefinitely in a high-security hospital “very probably for the rest of your life”.

He also ruled that Calocane should be subject to further restrictions if ever discharged from hospital, which would need to be approved by the Justice Secretary.

At a hearing on Wednesday, lawyers for the Attorney General’s Office argued that Calocane’s “extreme” crimes warranted “the imposition of a sentence with a penal element, an element of punishment”.

Neither the judge nor this court can ignore the medical evidence as to the offender’s condition which led to these dreadful events or the threat to public safety which the offender continues to pose.

Barristers for Calocane said that changing his sentence to a hybrid order would mean he would be “punished for being mentally ill”, with judges ruling on Tuesday that Mr Justice Turner made “no error”.

Giving their judgment, Baroness Carr, sitting with Lord Justice Edis and Mr Justice Garnham, said: “Because the offender’s level of retained responsibility was low, and in circumstances where the offending would not have taken place but for the offender’s schizophrenia, the judge was entitled to conclude that a penal element was unnecessary.

“This was so, despite the number of victims and the extent of the harm caused.”

She concluded: “It is impossible to read of the circumstances of this offending without the greatest possible sympathy for the victims of these terrible attacks, and their family and friends.

“The victim impact statements paint a graphic picture of the appalling effects of the offender’s conduct.

“Had the offender not suffered the mental condition that he did, the sentencing judge would doubtless have been considering a whole life term.

“But neither the judge nor this court can ignore the medical evidence as to the offender’s condition which led to these dreadful events or the threat to public safety which the offender continues to pose.”

Calocane, who attended via a video link from Ashworth high-security hospital near Liverpool, did not react as the judges gave their decision.

Dr Sanjoy Kumar and Dr Sinead O’Malley, the parents of Ms O’Malley-Kumar, also attended the hearing, while the relatives of Mr Webber and Mr Coates did not appear.

Speaking outside the Royal Courts of Justice following the decision, Dr Kumar said: “The Attorney General’s case has not been successful. This is disappointing, but not unexpected.

“The Nottingham attacks were entirely preventable. Nottinghamshire Police failed to produce a warrant for many months, a flawed investigation, no toxicology, over-reliance on psychiatric reports.

“Leicestershire Police failed to arrest Valdo Calocane. This is a failure of two police forces, a failure of the mental health trust, along with Nottinghamshire (County) Council as well.

“Missed multiple opportunities to prevent the Nottingham attacks and the murder of our children and Ian Coates is what has led us here today. We have continued to pursue agencies that failed us and hold them responsible for the Nottingham attacks so that no other family is made to suffer like ours.

“We thank everyone for the outpouring of support for our brave and beautiful daughter, Grace.”