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.
Britain's child sex abuse investigation body needs more access to phone and internet records so it can better investigate crimes, Theresa May has said.
The Home Secretary spoke ahead of reports the Government is due to pass emergency laws requiring phone companies to store text, call, and web use data.
Her comments came after it emerged the Child Exploitation and Online Protection Centre (Ceop) made fewer arrests last year than the previous year.
A review of undercover policing announced by the Home Secretary will initially focus on the Metropolitan Police's Special Demonstration Squad, a top secret unit that operated for 40 years before being disbanded in 2008.
It will also look at the activities of the National Public Order Intelligence Unit, which is not part of the Met but undertook similar tasks.
The investigation will look at a variety of issues, including what kind of undercover policing was undertaken, whether evidence relevant to criminal cases was kept secret and whether any convictions may be unsafe because undercover police activity was not revealed.
Speaking in a debate on passport delays, the Home Secretary, Theresa May MP, told the House of Commons:
– Theresa May MP, Home Secretary
Her Majesty's Passport Office is dealing with the highest demand for passports for 12 years, while the surge in demand usually experienced during the summer months started much earlier in the year. As a result, a number of people are waiting too long for their passport applications to be processed.
Ms May was speaking in a Commons opposition day debate called by Labour, in which many MPs highlighted the plight of constituents experiencing passport delays.
The Home Secretary has described forced marriage as "cruel and unacceptable" and said new laws will which come into effect today show the practice "will not be tolerated" in the UK.
In an exclusive blog for Good Morning Britain, Theresa May said laws were needed because the "scale of the problem is staggering".
– Theresa May
We want to send a clear message that forced marriage is cruel and unacceptable and will not be tolerated.
The individual stories are heart-rending. In one tragic recent case, a 17 year woman was taken to Turkey – she thought she was going on holiday, but instead she was forced to marry.
She was a bright, ambitious young woman who planned to go to university to study law. But suddenly her life had become a total nightmare. The marriage was horrifying, with sexual, mental and physical abuse.
Labour says Theresa May is still "failing to take responsibility" for the publication of a letter to colleague Michael Gove that appeared to accuse the Department for Education of failing to act over alleged extremist links in some Birmingham schools.
Following Ms May's statement to parliament today, shadow Home Secretary Yvette Cooper said: “The Home Secretary claimed she did not authorise the release of her letter to Michael Gove accusing his department of a failure to act to the media or on the Home Office website.
"Yet time and again she refused to answer whether she wrote it in order to leak it, who did release it and why she left it on the website for three days," she added.
“Theresa May didn't write or send the letter until after Michael Gove briefed the Times. Are we really supposed to believe she didn't write it in order to leak it?," Ms Cooper said.
Theresa May told the House of Commons that "action was taken immediately" on a private letter to Michael Gove that was published on the Home Office website.
Theresa May had questioned the Home Secretary on why the letter had been allowed to remain on the site for three days before it was removed.
Labour MPs have criticised Theresa May for "ducking" questions over who authorised the release of a letter she wrote to Michael Gove about alleged radicalisation in some Birmingham schools.
The Home Secretary told the House of Commons that she "did not authorise" the release of the letter but members of the opposition, including the shadow leader of the House of Commons Angela Eagle, complained she would not say who did.
Home Sec ducks the direct question on who authorised the release of the letter again #extremism
Teresa May still failing to reveal who authorised publication of her letter to Gove on Home Office website and why it stayed up for 3 days.
Theresa May refuses to say who authorised the letter on HomeOffice website. Evasion. If it was her that's a resigning matter.
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.