Emma Pattison, 45, her better half George, 39, and their girl Lettie, seven, were tracked down dead at 01:10 GMT on Sunday.
Surrey Police said they were called to the property by the South East Coast Emergency vehicle Administration.
Police said they were certain it was a disengaged occurrence "with no outsider inclusion".
An examination is being done to lay out the conditions of their demises.
Analyst Boss Examiner Kimball Edey said: "for Surrey Police, my group, and I, I first need to communicate my sincerest ...sympathies to the loved ones of Emma, Lettie, and George, as well with respect to the understudies and staff of Epsom School, for their appalling misfortune.
"I need to give my confirmation that we will lead an exhaustive examination concerning what occurred the previous evening, and expect to have the option to get some harmony in these horrible conditions. I would ask that their security is regarded at this extremely challenging time."
Ms. Pattison had worked at the esteemed non-public school for quite a long time, which was named the best free school of the year in 2022.
Expenses at the school are £42,000 each year for visitors or £28,000 for day understudies.
The seat of the leading body of lead representatives at the school referred to his late partner as "a superb educator, yet in particular, a wonderful individual".
"For the benefit of everybody at Epsom School, I need to convey our absolute shock and doubt at this lamentable news," Dr. Alastair Wells said.
"Our prompt contemplations and sympathies are with Emma's family, companions and friends and family, and to the numerous understudies and partners whose lives she advanced all through her recognized profession."
Examiner Jon Vale, Epsom and Ewell's district leader, said: "We're mindful that this appalling occurrence will have caused concern and upset in the nearby local area.
"While this is accepted to be a confined episode, before long our neighborhood officials will stay nearby to offer consolation to understudies, guardians, educators, and the neighborhood local area.
"I might want to thank the school and the local area for their comprehension and persistence while the examination proceeds."
Surrey Police added that the three passings have been accounted for to the coroner.
Surrey Police said they were called to the property by the South East Coast Emergency vehicle Administration.
Police said they were certain it was a disengaged occurrence "with no outsider inclusion".
An examination is being done to lay out the conditions of their demises.
Analyst Boss Examiner Kimball Edey said: "for Surrey Police, my group, and I, I first need to communicate my sincerest ...sympathies to the loved ones of Emma, Lettie, and George, as well with respect to the understudies and staff of Epsom School, for their appalling misfortune.
"I need to give my confirmation that we will lead an exhaustive examination concerning what occurred the previous evening, and expect to have the option to get some harmony in these horrible conditions. I would ask that their security is regarded at this extremely challenging time."
Ms. Pattison had worked at the esteemed non-public school for quite a long time, which was named the best free school of the year in 2022.
Expenses at the school are £42,000 each year for visitors or £28,000 for day understudies.
The seat of the leading body of lead representatives at the school referred to his late partner as "a superb educator, yet in particular, a wonderful individual".
"For the benefit of everybody at Epsom School, I need to convey our absolute shock and doubt at this lamentable news," Dr. Alastair Wells said.
"Our prompt contemplations and sympathies are with Emma's family, companions and friends and family, and to the numerous understudies and partners whose lives she advanced all through her recognized profession."
Examiner Jon Vale, Epsom and Ewell's district leader, said: "We're mindful that this appalling occurrence will have caused concern and upset in the nearby local area.
"While this is accepted to be a confined episode, before long our neighborhood officials will stay nearby to offer consolation to understudies, guardians, educators, and the neighborhood local area.
"I might want to thank the school and the local area for their comprehension and persistence while the examination proceeds."
Surrey Police added that the three passings have been accounted for to the coroner.
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