International efforts to resolve the crisis in Libya after the fall of Muammar Gaddafi must forge agreement between the warring parties to forestall the emergence of a failed state that could become a "Somalia-on-the-Mediterranean," the UK government's special envoy has urged.

Jonathan Powell, a veteran of the Northern Ireland peace process, warned in an interview to The Guardian that violent chaos in Libya will spread to its neighbours and to Europe and Britain if left unchecked.

Powell was speaking before news emerged on Sunday of the beheadings of 21 Egyptian Christians by Islamic State (Isis) fighters near Sirte and today's retaliatory bombing raids by the Egyptian air force on Isis training locations and weapons stockpiles in Libya.

The brutal killings and the continuing flight of migrants via the Mediterranean coast are bleak reminders of the repercussions of the country's breakdown. François Hollande, the French president, and Abdel Fatah al-Sisi, his Egyptian counterpart, called today for the UN security council to meet over Libya and to take new measures.

"Libya is in a downward spiral that we need to reverse and turn into an upward one," Tony Blair's former chief of staff told the Guardian. "There is a good deal of immediacy about this. But these things don't happen overnight. You've got to rebuild trust that has been badly broken."

Powell, appointed by David Cameron last spring, is talking to the armed groups that have pushed the oil-rich ​north African country to the brink since its 2011 revolution, Nato and Arab military intervention and bloody regime change.

Libya, he argues, has the advantage of not being plagued by religious sectarianism as most of its 6 million people are Sunni Muslims. "If you look down a telescope from Washington or London or Brussels it is easy to make all these places look the same," he said. "But this is a struggle for power and for money to a certain extent.

Powell is working with the UN envoy, the Spanish diplomat Bernardino Leon, on finding a way out of the current dangerous impasse. Less than half the protagonists showed up for two rounds of negotiations in Geneva. The turnout was better at a meeting last week in Ghadames in Libya- but they were still only "talks about talks."

The situation is complicated by the fact that the two main camps ​- Libya Dawn in Tripoli and the west, and Karama (Dignity) in the east ​- are in turn sub-divided into rival leaders, governments and militias, some of them Islamist. Others, like businessmen from the coastal city of Misrata, are keen to promote local agendas.

Now there is a new sense of urgency, said Powell, because of growing alarm about the rise of extremist and jihadi groups. ​Isis​ was blamed for the recent suicide bombing attack on Tripoli's most exclusive hotel. On Sunday it released a horrific propaganda video showing the beheading of the Egyptian Copts dressed in orange jumpsuits and described as "Crusader infidels" by their captors.

"Obviously it's difficult to tackle the terrorist threat unless you have a relatively strong government that everyone supports," the envoy said. "If you can get to a national unity government you can build other things on it. But to get a political settlement you also need some kind of pause in the fighting. So the objective is to get the armed groups to agree to that.

"Libya could, if it goes down this spiral, end up as a failed state. It could end up like a Somalia by the Med which would have very serious consequences for Tunisia, the one shining star that is left from the Arab spring, for Egypt, obviously, but also for southern Europe and eventually for us.

"The more there is an ungoverned space and a vacuum the greater chance there is of terrorists congregating there and mounting attacks. So far it's been attacks inside Libya... but if it does descend into a civil war the consequences for us will be very serious ​- not just in terrorism but in terms of people-smuggling, drugs and arms and everything else too. Libya is far too big to contain."