Philip Mitchell, 36, from Northwich, Cheshire, had access to his four children aged between six and nine but had failed to return them to their mother in the town after a trip out on Thursday.
The bodies of Jonathan, nine, his sister Cathryn, seven, and six-year- old twins Jessica and Christopher were found with their dead father in his Ford Fiesta by workmen arriving at the King Street industrial estate in Middlewich.
Police said they were not seeking anyone in connection with the deaths.
A Home Office pathologist was carrying out a post-mortem examination to find out how the five died.
Mr Mitchell lived in a flat in Arbor Close, Rudd Heath, Northwich, six miles from where the bodies were found.
Police have not revealed the name and address of the children's mother.
A spokesman said: "We are not looking for anybody else. A file is being prepared for the information of the coroner."
The mother was being spoken to by detectives trying to find the reason for the tragedy.Reuse content