The National College for School Leadership commissioned a survey of 1,100 parents to see what other professions they thought could make good heads.
School staff may be reassured that 19 per cent said teachers were the only people suitable the job.
But 21 per cent felt business leaders could be good heads. Other popular choices included police officers (15 per cent), university lecturers (11 per cent), and military officers (11 per cent) These professions beat school governors (9 per cent), doctors (6 per cent), politicians and lawyers (both 5 per cent).
The poll was carried out by the Ipsos MORI social research institute. Ben Page, its chairman, said: "It's all about discipline. They want to know their children are in safe, well-ordered environments and think behaviour is much more of a problem in schools than the heads who work there."