In the Commons on Thursday, Foreign Office minister Sir Alan Duncan said an internal Whitehall inquiry had found no evidence the leak was the result of computer hacking.
Instead he told MPs the focus was on finding "someone within the system who has released illicitly these communications".
The official inquiry will be led by the Metropolitan Police counter terrorism command, which is responsible for investigating breaches of the Official Secrets Act.
What is the Official Secrets Act?
The Official Secrets Acts 1911-1989 are used to protect state secrets and information which relates to the national security of the United Kingdom.
This includes matters of security, intelligence, defence, international relations and information which has been entrusted in confidence to another country.
It relates to those who work, or have worked, for the government and have access to sensitive information as part of their job.
The earlier version of the Act from 1911 protected whistleblowers from within the secret service on the grounds of public interest.
Do you have to sign it?
No. Signing has no effect on whether actions are legal or not. Signing the Official Secrets Act is often used as a reminder that you are under obligation to obey the law.
What is the penalty for breaking it?
Crimes relating to spying and sabotage carry the highest sentence, with a maximum jail term of 14 years.
Other breaches of the Act could lead to a term of up to two years in prison.
As such, if prosecuted and found guilty, anyone who leaked Sir Kim's memos could face anything from a fine to two years in prison if the leak was deemed "damaging".
Who has been found guilty of breaking it?
Several people have been found guilty of breaking the Official Secrets Act.
Sarah Tisdall, a clerical officer for the Foreign and Commonwealth Office, was found guilty in 1983 of leaking government documents relating to American nuclear weapons to the Guardian newspaper. She was sentenced to six months in jail.
Richard Tomlinson, a former MI6 spy, was imprisoned in 1997 after sending the synopsis of his book about his career in the secret service to an Australian publisher.
He served six months of a 12-month prison sentence after which the book was published in Russia and serialised in the Sunday Times newspaper.
In 2002, former MI5 officer David Shayler was sentenced to six months in jail after selling top-secret documents to the Mail on Sunday newspaper for £40,000.
The documents contained the names of secret service agents. After publication in 1997, he fled the country and was arrested upon his return three years later.
In 2003, Katharine Gun, a translator with the Government Communications Headquarters (GCHQ), was accused of revealing that US agents plotted to bug United Nations delegates to find out how they would vote on waging war against Iraq.
She was charged with breaching the Act after a memo, allegedly from a US National Security Agency official asking British counterparts to eavesdrop, was leaked to The Observer newspaper.
Charges were later dropped by the prosecution.
Former defence secretary Gavin Williamson was sacked in May after information was leaked from a top-secret meeting of the National Security Council about Chinese tech giant Huawei.
Allegations of breaching the act were brought against Mr Williamson.
But assistant commissioner Neil Basu said he was "satisfied" that the details disclosed to the media did not "contain information that would breach the Official Secrets Act".