The schools inspection criteria is "not fit for purpose" and greater local scrutiny is needed for England's free schools and academies, shadow education secretary Tristram Hunt has said.
It comes as 21 Birmingham schools are investigated after allegations of a takeover plot by hardline Muslims.
The Guardian says Ofsted is to rate one, Park View academy, as inadequate.
The Department for Education said all schools were required to offer a "broad and balanced curriculum".
Separately, Education Secretary Michael Gove said free schools were "proving an enormous success".
The school inspections follow claims hardliners were trying to take over some Birmingham schools, following the emergence of a so-called "Trojan Horse" letter - believed by some to be a hoax.
The document alleged there was a group of conservative Muslims attempting to usurp school governing bodies.
Speaking to BBC Radio 4's Today programme Mr Hunt said there needed to be a "local director of school standards" rather than trying to oversee schools from Whitehall.
Free schools and academies are independent of local authority control, and receive direct funding from the Department for Education.
Later in a speech to the centre-right think tank, Policy Exchange, Mr Hunt said no school should be judged "as good or outstanding" by Ofsted unless it delivered a "broad and balanced" education.
Under Mr Hunt's proposals, this requirement would be added to the core criteria against which schools are assessed.
The Ofsted report into Park View is expected to say the secondary school failed to adequately warn its pupils about extremism - two years after the school was considered to be outstanding by the education watchdog.
"How you can go from outstanding to inadequate? And that's because the inspection criteria is not fit for purpose," Mr Hunt told the programme.
By Alan Soady, Political Correspondent
This is not the first time in recent days that Labour has criticised the government over the fallout from the Birmingham schools allegations.
But the shadow education secretary, Tristram Hunt, is attempting to broaden the attack, focusing on the oversight of all free schools and academies in England.
It taps into a long-running political argument about the concept of free schools - and whether they can be kept in check centrally by the Department for Education rather than by local officials.
But the education secretary has robustly defended his sweeping changes to England's schools - changes which are central to his vision for education.
He will specifically address the question of oversight of schools in Birmingham when the Ofsted reports into the schools at the centre of the allegations are published next week.
Mr Hunt also accused the government of "incompetence" over its handling of the alleged Trojan Horse plot, saying the education department had failed to act when concerns about lack of oversight in schools were raised in 2010.
He said: "He [Mr Gove] must come to the House of Commons on Monday and place on record why he refused to act on warnings, why he rejects the evidence of the need for local oversight of schools, and why he thinks that more of the same is the answer."
In his own speech to the Policy Exchange, Mr Gove said claims that free schools and academies could go wrong "more quickly" were "the opposite of the truth".
"Academies and free schools are more accountable than local-authority maintained schools," he said.
Mr Gove was also asked on Saturday if he was considering his position in light of the row with Home Secretary Theresa May on how best to counter the threat of extremism in schools, to which he replied "no".
The two ministers have clashed over the handling of the Birmingham allegations, with the Home Office publishing a letter accusing the education secretary of failing to act.
Earlier, shadow home secretary Yvette Cooper said she believed neither Mrs May nor Mr Gove had got to grips with the issue of extremism.
She said there had been a lack of co-ordination across government, with the Department for Communities and Local Government being marginalised.
Cabinet Secretary Sir Jeremy Heywood has been asked to investigate the row between the home secretary and the education secretary.
Salma Yaqoob, a former Birmingham city councillor and the ex-leader of Respect, criticised the "hysteria" surrounding the Trojan Horse allegations.
She told the Today programme the "trickle" of leaked Ofsted reports, including Park View's, had "thoroughly damaged the reputation of Birmingham's schools and children", while there was still "no evidence" of a radical Muslim plot.
In a statement, the Department for Education said it was vital the Birmingham investigations were carried "impartially, without pre-judgment".
On Mr Hunt's criticism over free schools and inspections, it said: "All schools, including academies and free schools, are required to offer a broad and balanced curriculum.
"Ofsted's inspectors already consider how this is delivered and pupils' social, cultural, and moral development when deciding a school's rating."