David Cameron says 2011 can be year Britain 'gets back on its feet', but warns terrorist threat remains 'as serious as ever'

David Cameron has said 2011 will be a "difficult year", in his first new year's message to the country as prime minister.

He warned that the terrorist threat to the UK was "as serious as it ever has been", and stressed the need to counter extremism.

The Labour leader, Ed Miliband, used his own message to warn that 2011 would be a "year of consequences" for Britain, as a result of the government's decision to reduce the budget deficit at "an irresponsible pace and scale".

Cameron delivered his new year's message in a podcast posted on the official Downing Street website.

"2011 is going to be a difficult year, as we take hard but necessary steps to sort things out," he said. "But the actions we are taking are essential, because they are putting our economy and our country on the right path. Together, we can make 2011 the year that Britain gets back on its feet."

Cameron said "a lot of the heavy lifting" would happen during the next year. The full extent of the coalition government's spending cuts is expected to be felt more during 2011 than the previous eight months.

"Each and every minister in this government is acutely aware that the plans we have in place are tough, in fact incredibly difficult. But we're clear that the alternative – indecision and delay, would mean taking unacceptable risks with our economy, our country and our people," he said.

"I didn't come in to politics to make cuts. Neither did Nick Clegg. But in the end politics is about national interest, not personal political agendas."

On the subject of terrorism, the prime minister said: "Recent arrests show that that threat is still very much with us. And it is as serious today as it ever has been.

"We must ask ourselves as a country how we are allowing the radicalisation and poisoning of the minds of some young British Muslims who then contemplate and sometimes carry out acts of sickening barbarity. And the overwhelming majority of British Muslims who detest this extremism must help us to find the answers together."

Miliband said his thoughts were with those members of the armed forces who would continue to serve in Afghanistan through the year.

"Here at home, 2011 will be a year of consequences for Britain," he said. "Consequences that will be felt by hard-working families across the country. Consequences of the decision taken to reduce the deficit at what I believe to be an irresponsible pace and scale.

"Labour's challenge and duty in 2011 is to be people's voice in tough times and show that these are changes born of political choice by those in power not necessity. And we will take the next steps on the journey to win people's trust that we offer a better, more optimistic future for Britain."