The two inquiries, announced by Home Secretary Theresa May, will investigate alleged child abuse by MPs and wider public institutions.
The leaking, from her department, of a letter to Michael Gove, raises serious questions for the Home Secretary to answer.
One school was praised by Ofsted for using money from the pupil premium to pay for a number of cultural trips to Saudi Arabia.
Home Secretary Theresa May has denied Labour allegations that she broke the Ministerial Code and has demanded that the Shadow Home Secretary Yvette Cooper withdraw her comments.
Theresa May was unaware of the decision to publish a private ministerial letter she had sent to Education Secretary Michael Gove on the Home Office website last week, Downing Street has said.
ITV News Political Correspondent Libby Wiener reports:
Theresa May didn't know about her letter to Michael Gove on Brm schools being put on Government website, says PM's spokesman
Mohammed Shafique a governor from one of the schools in Birmingham at the centre of the Trojan Horse allegations has accused Ofsted inspectors of having an agenda against them.
Golden Hillock School in Sparkhill is one of six schools expected to be rated inadequate and placed in special measures when Ofsted's reports are published tomorrow.
21 schools were inspected following allegations of an extremist Islamic plot to seize control of the governing bodies.
Ofsted has declined to comment.
Home Secretary Theresa May will be called before the Home Affairs select committee to answer questions on her "unseemly" row with Education Secretary Michael Gove over claims that schools have been radicalised.
The committee's chairman, Keith Vaz, has written to Mrs May demanding a full explanation, and has also said there is a "strong case" to take evidence from her aide Fiona Cunningham who resigned as a result of the spat.
"We have conducted two inquiries relating to counter terrorism in the last two years which have emphasised the need for the whole of Government to work together," Mr Vaz said. "This unseemly row obscures the pressing issue of how to combat radicalism in schools."
Labour shadow Home Secretary Yvette Cooper has accused Theresa May of breaking the ministerial code, and called on her to explain her conduct.
Speaking to ITV News Political Correspondent Libby Wiener, she said
"We still have silence from the Home Secretary, even though the Education Secretary has apologised, and it does seem that she too has broken the ministerial code."
Toby Young, founder of the West London Free School, said the Home Secretary Theresa May reacted to criticism from the Education Secretary "like an Israeli tank commander being confronted by a stone-throwing Palestinian".
Speaking to Political Correspondent Libby Wiener he said Gove's comments show he is taking the issue of extremism in schools seriously, but it was a mistake to brief against Mrs May's counter-terrorism adviser, Charles Farr.
Yesterday Theresa May's special adviser Fiona Cunningham stood down over her part in the row.
The Foreign Secretary William Hague said the row between Home Secretary Theresa May and Education Secretary Michael Gove was a "disciplinary matter within the Government which the Prime Minister has dealt with in a very firm and clear way".
Speaking on the BBC1's Andrew Marr show, he said David Cameron was "making sure there was team discipline within the government" and that the Government would take a "robust" approach to extremism.
The row between Theresa May and Michael Gove over the handling of the allegations of an Islamist plot to takeover the running of Birmingham schools has led to the resignation of a close aide to the Home Secretary and an apology from the Education Secretary.
Here are some of the key developments in the feud between the Cabinet colleagues:
- November 2013: Mr Gove and Mrs May's dispute began when the Education Secretary called for the definition of extremism to be broadened so more hardline organisations were covered. Mrs May refused, leaving Mr Gove taking his argument to the Prime Minister.
- June 4 2014: On the day of the Queen's Speech, The Times reveals the extent of the row between the ministers. Mrs May questioned whether Mr Gove's department knew about the allegations in 2010 and asked: "If so, why did nobody act?" The duo issue a joint statement in a bid to dampen the story.
- June 5 2014: David Cameron vows to "get to the bottom" of the spat.
- June 6 2014: It emerges Cabinet Secretary Sir Jeremy Heywood is investigating the row for the PM.
- June 7 2014: Mrs May's special adviser Fiona Cunningham quits over comments in The Times and Mr Gove writes a letter of apology.
Labour's shadow minister for women and equalities has criticised David Cameron after Home Office adviser Fiona Cunningham resigned over a row about alleged Islamist radicalism in schools.
Gloria De Piero questioned why Michael Gove had apparently not been punished for "unauthorised comments" to newspapers, while the young aide had resigned.
So a young woman is hung out to dry while the man who caused the crisis in the first place carries on with impunity. Typical Cameron.
Shadow Home Secretary Yvette Cooper has questioned whether Theresa May authorised the leaking of a letter she wrote to Education Secretary Michael Gove.
Did the Home Secretary authorise the "improper release of correspondence between Ministers" that the No 10 statement refers to?
The private letter appeared in the media and seemed to show Ms May questioning Mr Gove's handling of alleged extremism in some Birmingham schools.