The bodies of Michael Pedersen, 51, his son, Ben, seven, and six-year-old daughter, Freya, were found next to a Saab 900SE convertible car in a lane in Newton Stacey, near Andover, Hampshire, on Sunday.
Mr Pedersen, a former sergeant in the Household Cavalry unit which was hit by an IRA nail bomb in London’s Hyde Park in 1982, had recently split from his wife, Erica, who lives in Ashford, Middlesex.
Caroline Dyer, headteacher of Ashford Church of England Primary School, said: “We are all deeply shocked and saddened at this news. The school is in contact with the relevant authorities but, as this is currently the subject of a police investigation, we are unable to make any further comment.”
Mr Pedersen, who also had two children from a previous relationship, wrote on Facebook on August 31 that he had split from his second wife, Erica, 43, with whom he ran a haulage business called High Road Logistics.
He said: “Worst day of my life. Sadly have split with Erica am absolutely distraught.”
Detective Superintendent Tony Harris, of Hampshire Police, said the “tragic” incident happened while the former serviceman was on an arranged visit with his two children.
Mr Pedersen, who had recently been living in Chertsey, Surrey, had taken Ben and Freya to visit his father in Andover but failed to return them to their mother by the pre-arranged time of 5pm. Their bodies were found lying behind the car at 6.15pm on Sunday by a walker, according to police.
Surrey Police said the case was being referred to the Independent Police Complaints Commission as the force have had previous contact with the Pedersen family.
A post-mortem examination found that Mr Pedersen died as a result of stab wounds to the chest, police said.