The head teacher of Epsom College made a distressed call to a relative before she and her daughter were shot dead by her husband, the BBC understands.
George Pattison is believed to have killed Emma Pattison and Lettie, seven, at the family home in school grounds before taking his own life.
Mrs Pattison is understood to have called the relative some time late on Saturday evening.
By the time the family member arrived, all three were dead.
The school announced on Tuesday it would close until after the half-term break, after “incredibly distressing” details emerged about how Ms Pattison died.
In a letter to parents, acting headmaster Paul Williams said: “Now is a time for families to come together and try and process this shocking news.”
He urged parents to keep a “close eye” on their children, adding: “The impact on your children cannot be underestimated and we are doing everything we possibly can to support them in whatever way they need.”
Surrey Police confirmed the family’s next of kin have been informed and are being supported by specialist officers.
Police said an investigation was being carried out to establish the full chronology and circumstances of the incident.
They confirmed a firearm, licensed and registered to Mr Pattison, had been found at the scene and has been recovered by officers.
However, causes of death will not be confirmed until post-mortem examinations have been completed later this week.
Mr Pattison’s gun licence had been recently updated.
Surrey Police made a routine phone call to the 39-year-old chartered accountant in the days preceding the killings, because the details of his new home address needed to be checked.
The force said that “due to the short period of time between that contact and this incident, we have made a referral to the Independent Office for Police Conduct (IOPC)”.
An IOPC spokesperson said: “We are assessing the available information to determine what, if any, further action may be required from us.”
It is understood that the couple was not known to Surrey Police.
Police also confirmed they were aware of “speculation” regarding a firing range at the school.
“We can confirm this range does not form part of our scene or our inquiries. Any reporting to suggest otherwise is inaccurate,” they added.
Det Ch Insp Kimball Edey said: “This is an incredibly traumatic incident and we are working around the clock to investigate and understand the exact circumstances which led to this point.
“We understand the public concern and upset, and we will clarify what we can, when we can, while respecting the right to a level of privacy for the families of those who have lost their lives.”
Mrs Pattison was appointed the first female head teacher of Epsom College five months ago. She has been praised for her dedication and inspirational leadership.
Prior to working at Epsom, Mrs Pattison spent six years as the head teacher of Croydon High School in south London.
Former colleague and friend Cheryl Giovannoni, said Mrs Pattison was a “adored” and a “real inspiration to those around her”.
The chief executive of the Girls’ Day School Trust, of which Croydon High School was a member, said Mrs Pattison “had this way of relating to people, she had such humanity”.
“She really understood what they were going through and she just worked so hard. She was so ambitious for the girls in her school and had this mission to make girls’ education forward-thinking and inspiring.”
Mr Pattison was a chartered accountant who was director of a management consultancy firm called Tanglewood 2016, according to Companies House.
In December, Mrs Pattison told a podcast run by students that her move had been “a really big change for my family”, adding: “I’ve got a new job, my husband got a new job, which wasn’t meant to happen, but did, and my daughter has started a new school.”
Boarding students at Epsom College pay more than £42,000 a year, and its alumni include Conservative MP Sir Michael Fallon, broadcaster Jeremy Vine and his brother, the comedian Tim Vine.
The school, which both boys and girls attend, was founded in 1855 and describes itself as being consistently among the UK’s leading schools, based on exam results.
Source : BBC