Brentwood MP Eric Pickles has been challenged to speak out following accusations the council's planning chairman bulldozed through an application for his political leader.
Liberal Democrat leader David Kendall has referred Cllr Kenny to the standards board for failing to declare his ties with council leader Cllr Brandon Lewis - although Mr Lewis did not personally submit the plans.
Cllr Kenny has been accused of rushing through the decision that allowed two outdoor classrooms on Green Belt land at Woodlands School in Hutton - where Cllr Lewis is a director.
Cllr Kenny has also been accused of not allowing opposition members to speak and failing to declare a personal and prejudicial interest. But he has denied any wrongdoing.