The school said it sought advice from the police after receiving a “high volume of direct correspondence and public social media posts”, which it said had been upsetting for staff, parents and governors.
A police officer issued a warning to the family in December, telling them to take their daughter out of school, which they did the next month.
But a week after that, on 29 January, Mr Allen said six police officers turned up at his home.
Mr Allen, who is a Times Radio producer and Liberal Democrat councillor on Hertsmere Borough Council, denied using abusive or threatening language, “even in private”.
He said a letter was sent by the chair of governors to all parents “warning them about what he described as inflammatory comments on social media”.
Mr Allen said: “When that was used in context with us, they never actually told us what it was we said that was so terrible, because they’ve never disclosed the WhatsApps that they got hold of.
“But when we look back through, the spiciest thing that we could find was Roslyn calling one senior person at the school a control freak, and that was the strongest remark we could find.”
