UK intelligence agents have been moved because Russia and China have access to classified information which reveals how they operate, a senior government source has told the BBC.
According to the Sunday Times, Moscow and Beijing have deciphered documents stolen by whistleblower Edward Snowden.
The government source told the BBC the countries "have information" that led to agents being moved but added there was "no evidence" any had been harmed.
Mr Snowden leaked data two years ago.
The former CIA contractor, now living in Russia, left the US in 2013 after leaking details of extensive internet and phone surveillance by American intelligence to the media.
His information made international headlines in June 2013 when the Guardian newspaper reported that the US National Security Agency was collecting the telephone records of tens of millions of Americans.
Mr Snowden is believed to have downloaded 1.7 million secret documents before he left the US.
The government source said the information obtained by Russia and China meant that "knowledge of how we operate" had stopped the UK getting "vital information".
BBC political correspondent Chris Mason said the problem for UK authorities was not only the direct consequence that agents had been moved, but also the opportunity cost of those agents no longer being in locations where they were doing useful work.
Analysis: By Gordon Corera - BBC security correspondent
The phrases "neither confirm nor deny" and "no comment on intelligence matters" is being used by government to respond to Sunday Times' story.
But my understanding from conversations over an extended period is that since he fled two years ago, British intelligence have worked on the assumption that Russian and Chinese spies might have access to his full cache of secrets.
Snowden has always maintained that there is no way that other states could do this but the spies are likely to have thought it too risky to take the chance. In turn, this may have led to undercover agents being moved as a precaution.
Snowden himself would not have had access though to any kind of database of MI6 agents but the fear might have been that by piecing together any secrets on how such agents communicate that were in the files, the Russians and Chinese might have been able to identify them.
However, no one in government today is confirming that they are sure that the Russians and Chinese have got full access - that remains in the realm of "no comment".
Intelligence officials have long warned of what they see as the dangers of the information leaked by Mr Snowden and its potential impact on keeping people in the UK safe - a concern Prime Minister David Cameron has said he shares.
According to the Sunday Times, Western intelligence agencies have been forced to pull agents out of "hostile countries" after "Moscow gained access to more than one million classified files" held by Mr Snowden.
"Senior government sources confirmed that China had also cracked the encrypted documents, which contain details of secret intelligence techniques and information that could allow British and American spies to be identified," the newspaper added.
Tim Shipman, who co-wrote the Sunday Times story, told the BBC: "Snowden said 'nobody bad has got hold of my information'.
"Well, we are told authoritatively by people in Downing Street, in the Home Office, in the intelligence services that the Russians and the Chinese have all this information and as a result of that our spies are having to pull people out of the field because their lives are in danger.
"People in government are deeply frustrated that this guy has been able to put all this information out there."
The newspaper quoted Sir David Omand, former director of UK intelligence agency GCHQ, saying the fact Russia and China had the information was a "huge strategic setback" that was "harming" to Britain, the US and their Nato allies.
The former head of the Navy and current Labour peer Admiral Lord West called Mr Snowden a "traitor", saying it was now much harder to monitor terrorists and criminals.
Professor Anthony Glees, of the University of Buckingham's Centre for Security and Intelligence Studies, said the leaking of the documents had been "very, very damaging".
He told the BBC: "From the documents that Snowden has, it will be possible to identify those very brave people in countries where if you spy for Britain you get killed.
"There may even be names inadvertently included... Edward Snowden is not only a villain, he's a villain of the first order."
But, the director of Liberty, Shami Chakrabarti, said that if Mr Snowden had been pardoned in the US "for doing what many in the United States (consider) to be a public service in revealing the sheer extent of mass surveillance, he wouldn't have needed to go to Russia".
'Pinch of salt'
It comes two days after the UK's terrorism watchdog David Anderson QC published a review into terrorism legislation, which was set up amid public concerns about surveillance sparked by Mr Snowden's revelations.
He said the country needed clear new laws about the powers of security services to monitor online activity and concluded that the current situation was "undemocratic, unnecessary and - in the long run - intolerable".
Former Conservative cabinet minister Andrew Mitchell told BBC Radio 5 Live's Pienaar's Politics that the timing of the story was "no accident".
"This debate in Britain between individual liberty and collective security comes into very sharp focus as a result of the Anderson report, and that is why [The Sunday Times' Tim Shipman] has got his very good exclusive today."
Asked if it was part of a propaganda drive by the government, he replied: "Well, there is a big debate going on, you know," adding: "Anderson is going to be a very important part of that".
Like it or not, he said, Snowden had directly engendered "a massive change of view about the debate" in the US.
Meanwhile, civil liberties campaigner David Davis - also a Conservative MP - told the Guardian the story should be treated with "a pinch of salt".
"You can see they have been made nervous by Anderson. We have not been given any facts, just assertions," he said of the government.
The government is preparing new legislation to give police and agencies more tools to monitor online communications data, saying this is necessary to fight terrorism.
Previous attempts were blocked by the Lib Dems in coalition, and critics say the plans amount to a "snoopers' charter".