Dmitry Medvedev today accused government officials of allowing security checks at Domodedovo airport to slip into "a state of anarchy", amid reports that a Black Widow suicide bomber detonated the bomb that killed 35 people there yesterday.

The Russian president told chiefs of the federal security service (FSB) that those responsible for transport security "could be dismissed or face other sanctions" as a result of the negligence.

"We will have to put in place a much tougher inspection system, total inspections. It will likely take passengers longer, but it's the only way out," he said. "The information available to us [from Domodedovo] suggests that it was simply a state of anarchy. People were able to enter [the airport] from any place. Control over people's movements was partial and did not apply to those waiting for passengers."

Medevedev said earlier in the day: "What happened shows that there were clear security violations."

The massive blast took place at about 4.30pm beside the international arrivals hall at Moscow's busiest airport. The bomb, packed with nuts, bolts and ball bearings, ripped through the area, wounding up to 180 people.

A Briton killed in the attack was named today as Gordon Campbell Cousland. A second victim thought to be British turned out to be a Russian with dual Hungarian nationality. James Barbour, a spokesman for the British embassy in Moscow, said: "We are checking all hospitals to establish if there are any British citizens among the injured."

A source close to the investigation told the RIA Novosti news agency that the bomb was detonated by two people. "The blast occurred when a suspected female terrorist opened a bag. She was accompanied by a man whose head was ripped off by the explosion," the source said.

Investigators had earlier suggested that a man aged 30-35, whose remains they had collected, was the bomber.

The source added: "It cannot be ruled out that the terrorists wanted to leave the explosive device in the hall but the bomb was detonated inadvertently or by a remote control device.

"The terror attack was carried out according to a scheme that is used by terrorists from the north Caucasus region," he said. "The blasts at the Rizhskaya subway station [in 2004] and other explosions in the Moscow metro [in 2010] were carried out similarly, when the terrorists were accompanied by militants."

The so-called Black Widows are women who become suicide bombers, often after their husbands and brothers are killed by security forces in Chechnya and other southern Russian republics gripped by Islamist insurgency.

It appeared the attackers were able to move freely to the point of detonation because there were no metal detectors at entrances to the airport.

Medvedev said it was "our misfortune" that increased security measures introduced after two planes that took off from Domodedovo were blown up in mid-air in 2004 had failed to prevent yesterday's blast.

"It is not so easy to carry such a large amount of explosives [into an airport]," he told reporters. "Everyone who has anything to do with the company who is in charge of making decisions there, as well as the management of the airport should be held to account for it."

Gennady Gudkov, a KGB veteran who is deputy head of the Duma's security committee, said the attack showed the failure of the Kremlin's anti-terrorism efforts.

"There is now a queue of suicide bombers in the north Caucasus who are ready to blow themselves up wherever you like," he told the Kommersant newspaper.

Law enforcement agencies "think they can ensure greater security by increasing the number of block-posts, passport checks and constant searches, but that's not the case," he added. "The most important thing is to establish a network of agents and informers."

Vladimir Ovchinsky, a former head of Russia's Interpol bureau, said the attack was enabled by "criminal negligence" on the part of commercial and state security agencies.

"In reality, we need to admit that we have been at war with separatists and terrorists in the north Caucasus for almost 20 years," he told the Guardian. "After the wave of suicide and other attacks in Russia last year there was a desperate need to increase security at all points where the public concentrates in high numbers, including airports. That didn't happen."

Referring to Moscow's other main air hub, he said: "I fly often from Sheremetyevo and Domodedovo myself and I would call the security system in both disastrous."

There were reports today that the Domodedovo blast may be linked to an incident in eastern Moscow on 31 December when a bomb exploded in a house, killing a woman. Police later established she was a suicide bomber sent by Dagestani militants to attack the capital and who had mistakenly activated the device.

Russian media said the militants may have sent other bombers to Moscow in December, who could have targeted the airport yesterday.