George Pattison is thought to have shot Emma Pattison, 45, and their daughter Lettie, seven, with his shotgun at their home on school grounds last weekend.
Pattison’s uncle Frederick Cameron, 83, said his nephew “must have been in a state of madness”.
Speaking to the Mail on Sunday, Mr Cameron said: “He didn’t strike me as anyone who would do anything of that nature.
“He must have been in a state of madness... It doesn’t make any sense to me.”
Mr Cameron added that he first learned of the deaths through his daughter Suzette, who is Pattinson’s cousin.
“From what Suzette said it seems like there were problems [in the marriage]… But that doesn’t mean you shoot people,” he told the paper.
Surrey Police has said Mr Pattison legally owned a gun that was discovered at the scene of the tragedy and the force has launched a homicide investigation.
The deaths are being investigated as a possible murder-suicide.
Mr Pattison had been in contact with Surrey Police just days before the killings about his gun licence in order to change his address after the family moved to the school site from Caterham.
The force referred itself to the Independent Office for Police Conduct (IOPC) due to its contact with him on February 2.
But on Friday, an IOPC spokesperson said: “We received a mandatory referral from Surrey Police on February 5 related to the deaths of Emma, Lettie and George Pattison.
“We have reviewed the recent contact Surrey Police had with Mr Pattison regarding his firearms licence and have decided that no investigation is required.
“Following a thorough assessment of the available evidence, we determined on February 8 that the matter should be returned to the force to handle as it deems appropriate.
“We have reminded the force of its obligations, and that if evidence were to come to light that anyone serving with the police may have breached standards of professional behaviour or committed a criminal offence in connection with this, they should refer relevant matters to us.”
