George Pattison is said to have killed Emma Pattison and their seven-year-old Lettie at the family home on school grounds.
Mr Pattison's gun licence had been recently updated.
Mrs Pattison made a distressed call to a family member some time late on Saturday evening. By the time the relative arrived, all three were dead.
Mrs Pattison was appointed the first female headteacher of Epsom College just five months ago. Prior to working at Epsom, Mrs Pattison had spent six years as the principal of Croydon High School in south London.
Mr Pattison was a chartered accountant who was director of a management consultancy firm called Tanglewood 2016.