The parents of a troubled teenager at a Westbury school who killed herself in similar horrific circumstances to a school friend spoke of their frustration that those responsible for sexually abusing their daughter have not been brought to justice.

Scott and Sue Stroman, of Haringey, north London said their 16-year-old daughter Mary was subjected to a "terrible sexual trauma", which probably involved an older man or men - leading to a serious deterioration in her mental health.

"Rather than apportion blame, it is our wish to bring attention to these issues in the hope that other children in similar circumstances can benefit," Mr and Mrs Stroman said after a coroner concluded Mary had taken her own life.

"Mary herself would never reveal the details of what happened to her and without her co-operation the Metropolitan Police felt they could not pursue an investigation, even though we were able to provide times, dates, physical evidence from phones and computers and even clothing.

"It was and is a cause of continuing frustration and sorrow to us that nothing could be done to try and identify the perpetrators of these crimes - both for Mary's sake and for that of other children who may similarly be at risk."

Mr and Mrs Stroman also criticised the 13-month delay in Haringey Council funding a therapeutic residential placement for Mary.

"The continual delay seriously impacted her mental health, providing her with constant false hopes, repeated disappointments and a deterioration of trust - leading at times to despair," they said.

"In the meantime, Mary had suffered many further months of grief and mistrust, had been subjected to a further series of assessments and had been assigned a changing series of social workers, forcing her to 'tell her story' over and over. She was tired and tormented and lost confidence in the fact there was a way forward for her.

"Though we feel the individuals who dealt with Mary from Haringey social services were sympathetic and professional, we found the overall quality of service that we received was very seriously lacking. The workings of the machine and bureaucracy were insufficient."

Mr and Mrs Stroman added: "It is a terrifying prospect that our beautiful daughter and other children like her could ever choose suicide as a potential solution to life's challenges.

"As we begin to come to terms with life without Mary our hope now is that lessons can be learnt from her tragic story. She was a much-loved and unique member of our family and we miss her terribly."

Mary was the youngest of five children of Mr Stroman, a renowned jazz musician, composer and conductor, who is one of the most prominent figures in London's jazz scene, and his wife, a nurse.

The hearing in Salisbury heard that Mary killed herself on January 15 this year - two days after the inquest had begun into the death of her friend Tallulah Wilson, 15, who died at London's St Pancras station in October 2012 after also being struck by a train.

Both teenagers attended St Marylebone School and were classmates, playing in the orchestra together, with Mary playing the piano and viola.

Mrs Stroman said: "Tallulah played on Mary's mind and if we were going through King's Cross Mary would say 'This is where Tallulah died'."

At the time of Mary's death she was a pupil at the Tumblewood Community School in Westbury, a residential school for adolescent girls with emotional and behavioural difficulties.

The decline in her health had begun after she told friends she had been sexually abused and was later diagnosed with post-traumatic stress disorder after several incidents of self-harming.

The inquest heard that the driver of the First Great Western service from Portsmouth to Bristol Temple Meads saw a figure on the railway line but was unable to stop in time.

A post mortem examination found Mary had died instantaneously from multiple injuries.

Wiltshire and Swindon coroner David Ridley concluded Mary had taken her own life while suffering from complex post-traumatic stress disorder but insisted there was no evidence to link her death to Tallulah's.

"I am satisfied on the balance of probabilities that it is entirely appropriate to make a finding of fact that Mary suffered severe mental trauma, more likely than not as a consequence of previous episodes of sexual abuse," he said.

"However, due to Mary's reluctance to disclose these details, details of exactly when and where these incidents occurred are unclear but I am satisfied she suffered mental trauma as a consequence of these episodes.

"I make no finding that anyone ought to have known that Mary was going to take her own life. Tragically, I fear what happened was spontaneous."

The coroner said the notes Mary left behind in her room did not mention Tallulah at all but did refer to the "perpetrators of abuse".

"Although they were friends at school there is no evidence before me that allows me to make a finding of fact that these two deaths were linked," Mr Ridley said.

"In my judgment any link would have to be as a result of pure speculation. We will never know what happened and what triggered Mary to take the action she did. Possibly it was a flashback in relation to the post-traumatic stress disorder but there is no evidence before me and it would be pure speculation.

"Whatever triggered her actions it sadly resulted in the violent and tragic death of Mary."

Mr Ridley added that he would be sharing his conclusions with both Haringey Council and the Met Police.

After the inquest, Tumblewood Community School released a statement, which expressed sincere condolences to Mary's family for her death.

"Mary was a popular and bright member of the community with a good sense of humour," it said.

"She was an accomplished artist and musician and had an affinity with animals, especially horses. Mary is greatly missed by staff and children."

A Haringey Council spokesman said: "This was a tragic incident and our thoughts are with Mary's family at this difficult time.

"This was a complex and difficult case and we worked closely with Mary's family on decisions relating to her care.

"We'd urge anyone affected by the issues raised by this case to speak to family and friends or seek confidential support from counselling professionals.

"It would be inappropriate to comment further at this time."