Heads' leaders are calling for all Ofsted school inspections to be led by elite HMIs (Her Majesty's Inspectors).
The pressure for the change follows the dramatic increase in the proportion of schools being failed under the watchdog's new inspection framework.
The two headteachers' associations believe the increase is partly due to inspectors' belief that they have to follow the framework to the letter.
They think that highly trained HMIs, directly employed by Ofsted, are more likely than "additional inspectors" employed by external contractors to have the confidence to treat the framework as guidance that is open to interpretation.
Mick Brookes, general secretary of the NAHT, said: "The thing about HMIs is there is the quality assurance in terms of training and standards which we don't necessarily believe is there with other inspectors, although there are some very good teams out there."
At the moment, according to Ofsted three quarters of secondary inspections, 85 per cent of visits to schools causing concern and a "substantial minority" of primary inspections are led by HMIs.
Ofsted says its additional inspectors are trained and extensively mentored for the new framework and that no inspectors can carry out visits without supervision until HMIs have declared they meet the required standard.
But Malcolm Trobe, policy director at the Association of School and College Leaders, said: "We would like to see all inspections led by HMIs because there is a clear rigorous assessment process on appointment of HMIs.
"Whereas there are very many good additional inspectors leading inspections, they do not go through the same process before appointment as HMIs do."
In January, the Commons schools select committee called for Ofsted to "aspire" to make all inspections HMI-led and said that "schools causing concern should always be inspected by a team headed by an HMI".
Estyn, Ofsted's Welsh counterpart, plans to introduce HMI-led inspections gradually from September as part of a new inspection framework.
The first term of Ofsted's new regime, introduced last September, saw the proportion of schools rated inadequate more than double and the proportion rated outstanding more than halve. The watchdog said this was partly due to a greater focus on weaker schools.
Ofsted currently has 245 HMIs inspecting schools with 1,567 additional inspectors.
Mr Brookes said that if the watchdog introduced a system with even less time spent on good schools it would be possible for all inspections to be HMI-led.
An Ofsted spokesperson said: "We are concerned about the feasibility of the suggestion and estimate that it would require the recruitment of a minimum of 150 extra HMIs.
"Ofsted does not believe that there would be any great advantage to having all inspections led by HMIs - particularly if this diminished their critical role in quality assurance."