Britain's economy will be hit hard by further turmoil in the eurozone, David Cameron has warned, despite widespread relief on world financial markets as a new leader was installed in Greece and Italian politicians backed harsh austerity measures.

The prime minister insisted a "big question mark" remains over the future of the single currency, amid signs that the political impasse in Italy that sparked panic among investors may be close to a resolution. George Osborne, the chancellor, described events on the continent as "dangerous", adding: "There's no doubt that growth in Britain, jobs in Britain, have been hit by what's going on in the eurozone."

The fragile state of Britain's economy will come back into focus next week, with the latest jobless figures expected to show that public sector job cuts and the collapse of confidence among businesses have caused unemployment to rise rapidly.

The number of young people out of work is expected to hit 1 million, and with Osborne due to deliver his autumn statement on 29 November, pressure is increasing on the government to take urgent action to boost economic growth. The deputy prime minister, Nick Clegg, tells today's Times that Osbornes's autumn statement must deliver for the young, adding that it is "morally imperative" for the government to act.

The chancellor made clear that he intends to blame events across the Channel for the deteriorating economic outlook and to insist that deviating from his deficit-cutting strategy would expose the UK to the kind of loss of investor confidence faced by Italy in recent days.

"It's all the more reason that we in Britain weather this storm by taking the difficult decisions we take on our own terms – rather than being forced to do so by the markets," he said.

The prime minister told Radio 2's Jeremy Vine show that if UK interest rates hit Italian levels, it would be "calamitous". "If we risked spending a lot more money or giving up on our plan to get on top of our debts and our deficit, interest rates could go up, mortgage rates could go up. That would be the worst thing for family finances."

But Labour accused Cameron of being "irresponsible" after he conceded that, despite his public exhortations to Germany to allow the European Central Bank to bail out debt-ridden states to calm the crisis, he had not spoken to Angela Merkel or Nicolas Sarkozy for the past three days. His official spokesman conceded that no conversations were planned for the weekend either.

"This laid-back attitude from our prime minister is now so out of touch with the needs of businesses and hard-pressed families, it is becoming deeply irresponsible," said Rachel Reeves, the shadow chief secretary to the Treasury.

Cameron's spokesman insisted that "the action lies with the eurozone to implement the package that it has agreed. What the prime minister is focused on is ensuring that we protect the UK economy from the global economic storm." He added that the eurozone needed "action, not further meetings".

Former central banker Lucas Papademos was sworn in as prime minister in Greece with a promise to implement the reform measures and spending cuts demanded of the country as part of the latest international bailout package agreed in Brussels earlier this month.

In Rome, the centre of this week's market turmoil, the senate passed a controversial package of reform measures. The lower house is expected to follow suit in a special session on Saturday, clearing the way for the former European commissioner Mario Monti to take over as the leader of a so-called technocratic government.

Financial markets were reassured by events in Greece and Italy, with the FTSE100 closing up just over 100 points, or 1.85%, at 5545.38, while the German Dax, rose by 3.2%. The Dow Jones in New York rose 259 points or 2.2%.

There was a welcome decline in the Italian bond yield – the interest rate the embattled government pays on its debts – which jumped above 7% on Wednesday, the level that triggered bailouts for Ireland, Portugal and Greece. By the end of Friday, yields had declined to 6.47%. However, economists are warning that even if the immediate crisis is over, confidence has been shaken by the events of recent days, and the eurozone economy is heading for a double-dip downturn.

Michael Saunders, European economist at Citigroup, said that since the onset of the recession that followed the collapse of Lehman Brothers three years ago, the UK and the rest of Europe had lived through the early part of a "lost decade" like the prolonged period of stagnant growth experienced in Japan from the early 1990s. "For Europe and the UK, this will be about as bad as anything Japan experienced."

Jonathan Loynes, European economist at Capital Economics, said: "There still seems to be extraordinary complacency about the effect all this will have on the eurozone. All the indicators are pointing to a deep recession, and all that's without the euro blowing up. If the euro blows up, it's another Lehman, or even bigger."

He said the Treasury could be forced to take fresh emergency measures to prop up the financial system if the crisis worsens. "It's very likely that there will need to be more support for banks."