, he said it was time to consider whether the close focus on English and maths in inspections was "at the expense of" other subjects and failed to prepare children adequately for secondary school.
The former headteacher said the watchdog's new inspection framework, introduced this month, placed greater weight on the wider curriculum in primary and secondary schools. A consultation on the future of inspection, due to start next month, would ask teachers and schools "if we need to do anything further in that area", he added.
"We must continue to emphasise the importance of English and maths [in primaries], but we should not do that at the expense of other subjects," Mr Cladingbowl argued. "There will be certain circumstances where it's right for children to be given additional help with English and maths at the expense of something else, to get them to a point at which they can access the curriculum properly.
"But, through our consultation, we'll want people to ask themselves searching questions about to what extent that should happen. At what point should it stop?"
Although it was right that inspectors had in the past focused on English and maths in primary schools, Mr Cladingbowl said Ofsted now favoured a "broad and balanced" curriculum that did not "limit children's experiences or.fail to prepare children for secondary school and for life in modern Britain".
"We want to look and see if we've got the balance right between the core subjects and the foundation subjects; between English and mathematics, and art, history, music, geography and so on," he added.
A new national curriculum for primary and secondary was introduced this month. The demands in maths have increased for primary pupils: under the previous curriculum, for example, children were expected to know their times tables up to 10 by the age of 9, but they are now expected to be proficient up to 12x12.
Tony Draper, headteacher of Water Hall Primary School in Milton Keynes, said that although a change in approach might be beneficial for pupils and teachers, it could lead to the creation of "another hoop for schools to jump through".
"There's not a headteacher in the country who would not embrace a focus on a wider curriculum: on music, drama, the arts and creativity," he said. "We want to develop children for secondary education and to go out into the wider world. We want to develop musicians, dancers, people who are skilled in the creative arts.
"But we need to make sure this doesn't lead to a new layer of inspection, but is a fundamental move away from this condemnation by data. Inspection is currently so focused on English and maths that schools in challenging circumstances are focused on it to the nth degree, to the detriment of other subjects."
Russell Hobby, general secretary of the NAHT headteachers' union, warned that the impact of the move would be limited by government-imposed floor standards at the end of primary school that applied only to English and maths skills.
From this year, at least 65 per cent of a school's pupils will be expected to achieve level 4 in maths, reading and writing, and children must make sufficient progress. Schools that fail to hit these targets could be at risk of forced academy conversion.
"What Ofsted focuses on tends to get done, but floor standards for English and maths are still a powerful driver that is out of Ofsted's control," Mr Hobby said. "Another problem is that there are not enough primary specialists carrying out inspections, meaning the task often falls to inspectors from the secondary sector who are unable to make the intuitive judgements that are required to assess subjects which are not tested."
The implications of a shift in approach by Ofsted would also be significant for secondary schools, according to Brian Lightman, general secretary of the Association of School and College Leaders.
"It's essential that English and maths remain key areas of focus so that children arrive in secondary school able to cope," he said. "There's also a danger that Ofsted must define what a rich and broad curriculum looks like. The government policy has been to give schools flexibility to decide; this could actually reduce it."
`It's not an eitheror issue'
Ruth Whymark, headteacher of Cranmer Primary School in Mitcham, South London, believes that although literacy and numeracy are "vital" for primary pupils, other subjects should not be squeezed out.
"My school is very holistic in its approach, with a real focus on the arts," she says. "A wider curriculum is important, but good standards of English and maths are vital for ensuring young people improve their life chances. It's not an eitheror issue; it's important we have both.
"We need to make sure children have high levels of reading, maths and writing ability but are also able to experience a broad and rich curriculum. Having Ofsted focus on this breadth is important, given that academies don't have to follow the national curriculum," she adds.
"Children do have a dearth of cultural experiences. Wimbledon - a mecca for the arts, tennis and wider cultural experiences - is just down the road from us, but in Mitcham children don't have access to these things. School is the only place where they can experience them. If schools have a narrow focus on achieving level 4s for their pupils, they sell themselves short."