A report recounting a litany of near-misses in which nuclear weapons came close to being launched by mistake concludes that the risk of potentially catastrophic accidents is higher than previously thought and appears to be rising.

Too Close for Comfort: Cases of Near Nuclear Use and Options for Policy, published by Chatham House, says that "individual decision-making, often in disobedience of protocol and political guidance, has on several occasions saved the day", preventing the launch of nuclear warheads.

The report lists 13 instances since 1962 when nuclear weapons were nearly used. In several cases the large-scale launch of nuclear weapons was nearly triggered by technical malfunctions or breakdowns in communication causing false alarms, in both the US and Russia. Disaster was averted only by cool-headed individuals gambling that the alert was caused by a glitch and not an actual attack.

The Chatham House authors say the risks appear to be rising. Nuclear weapons are spreading – most recently to North Korea – and disarmament is stalling. Russia and the US still have an estimated 1,800 warheads on high alert, ready to launch between five and 15 minutes after receiving the launch order – a fact that becomes all the more significant with rising tensions over Ukraine.

"The question today is: are these risks worth it?" said Patricia Lewis, Chatham House research director for international security and one of the report's authors. "You can imagine a situation in which tensions rise and signals come in and people misinterpret what is going on. Will people always have sound enough minds to take the time to make a reasoned decision?"

The mental state of some of the leaders who had their fingers on the nuclear button has sometimes been a source of worry. Richard Nixon and Boris Yeltsin both raised concerns among their top advisers with their heavy drinking. In May 1981 the newly elected French president, François Mitterrand, left the French nuclear launch codes at home in the pocket of his suit.

President Jimmy Carter did the same in the 1970s, and the suit as well as the codes were taken to the dry cleaners. The US launch codes went missing again when Ronald Reagan was shot on 30 March 1981. FBI agents had them, along with the injured president's bloodied trousers.

Monday's report focuses on cases in which nuclear weapons came close to being launched deliberately on the basis of bad or incomplete information. However, there is an additional risk of accidents inherent in the maintenance of stockpiles of more than 17,000 warheads held by Russia, the US and the other seven nuclear-armed states.

Some of those accidents were described in a book published last year, entitled Command and Control.

Author Eric Schlosser gives an account of an incident in September 1980 in Damascus, Arkansas, in which a maintenance engineer dropped a socket wrench into a silo holding a Titan II nuclear missile, igniting its fuel and triggering an explosion which sent the warhead flying. It landed near a road but did not detonate.

In an earlier accident in January 1961, a B-52 bomber broke up over North Carolina, dropping its two nuclear bombs over the town of Goldsboro. One of the bombs activated, engaging its trigger mechanism. A single low-voltage switch was all that stood between the eastern US and catastrophe.

Whoops apocalypse

These are some of the incidents that illustrate how close the world has come to accidental nuclear apocalypse:

Washington, June 1980 A faulty computer chip triggered a nuclear attack warning on the US, giving the impression that more than 2,000 Soviet missiles were on the way.

Cuba, October 1962 Four nuclear-armed Soviet submarines were deployed in the Sargasso Sea at the height of the Cuban missile crisis. US warships had warned Moscow that they would be practising dropping depth charges, but the message did not reach the submarines. With his communications cut off and believing himself under attack, one commander ordered a launch of nuclear warheads, declaring: "We're going to blast them now." He was persuaded to desist by his second-in-command.

Soviet Union, September 1983 Shortly after midnight on 25 September an alert sounded at a Soviet satellite early warning station. The data suggested five intercontinental ballistic missiles were heading towards the country. Lieutenant Colonel Stanislav Yevgrafovich defied protocol by not reporting the incident to his superior, gambling that it was a false alarm. It turned out that sunlight glinting off US territory had confused the satellite.

Russia, January 1995 On 25 January Norwegian scientists launched a Black Brant rocket to study the aurora borealis over the Svalbard region. They warned Moscow but the message never reached the radar operators at the Russian early warning stations, who mistook the rocket for an incoming Trident submarine-launched missile. President Boris Yeltsin was discussing his decision with his top military commander when the rocket fell wide of Soviet territory.

• This article was amended on 30 April 2014 to correct the spelling of Mitterrand.