The group may not have appeared on Top of the Pops, but it has performed in front of 270 screaming teachers in a primary school and is gaining a growing fan-base in the staffrooms of Barnet.
The rock-star heads say that being in the band allows them to escape from the pressures of their jobs. Yet their daily frustrations have inspired some of Squawking Heads' lyrics - which include language they would be appalled to hear from their own pupils.
The recent Wheatus hit, "Teenage Dirtbag", has been transformed into "Teacher Dirtbag", an impassioned ode to Estelle Morris, which is unprintable in a family newspaper.
Even Pink Floyd's classic attack on education, "Another Brick in the Wall", has been customised.
One verse now goes: "We don't need no standards funding No design and build, no CEA Scrap league tables, restore our values We need a rise not performance pay."
Singer and guitarist Neil Marlow, head of Moss Hall junior school, said the eight heads decided to form the group while on a residential training course last year.
Mr Marlow, 39, said: "One of the heads had heard I was in a band and asked me to bring along my guitar. Over drinks in the bar we started singing together and someone said: 'Let's form a band'."
Joining Mr Marlow in the group is Jude Hall of Tudor school on keyboards, Steve Hilbourne of Manorside on bass guitar, Steve Williams of Goldbeaters on rhythm guitar, Duncan Mills of Holy Trinity on guitar, with Phil Elgar of Trent primary, Lynda Warrington of St John's infants, and Bob Cooper of Parkfield on vocals.
The eight heads are supported by a parent-governor on drums, while an ex-school caretaker takes charge of their lighting.
"We're not planning to release any of the songs," Mr Marlow said, "But I think we're still pretty good."
FUTURE SQUAWKING SONGS?
* I Can't Get No SATisfaction
* This Year 4's Love
* Re-re-ception, When The Crowd Say Bo Selector
* Only 24 Literacy Hours From Tulsa
* Can't Get You Out Of My OFSTED
* I'd Do Anything For Love, But I Won't Do SATs
* Pre-Teenage Kicks
* Like a Bat Out Of Estelle
* Paperwork Writer
* I Can Feel No Funding From The Blair Tonight
* They Call Me Mr Scholastic, Reading's Fantastic
* Just The Key Stage Two Of Us