PM says economic crisis will go on for years and progress on reducing dependence on City and public sector too slow

David Cameron on Sunday held out the prospect of the UK economy being dragged down for years, as he predicted the euro crisis was "nowhere near half complete" and warned the single currency may yet break up. He also admitted efforts to move the UK economy away from dependence on the City and the public sector were not going fast enough.

Speaking at the start of a week of elections in Europe, including for the French presidency and the Greek parliament, Cameron's suggestion that governance of the euro is not yet resolved will anger the German chancellor, Angela Merkel, as she seeks to steady increasingly nervous markets.

Cameron's dire warning about the euro in part reflects a desire to explain that the continued problems in Britain's main export markets had led the UK last week to slip back into recession. Asked if the world was halfway through the crisis in the eurozone, he told BBC1's The Andrew Marr Show: "I don't think we're anywhere near halfway through it."

Many commentators would argue the eurozone crisis started in late 2009, implying that Cameron believes it will stretch on for many years. Describing "massive tensions" inside the eurozone, he said: "I think it's going to be a very long and painful process in the eurozone as they work out do they want a single currency with a single economic policy and all the things that go with it, or are they going to have something quite different? That, they have to decide about."

He said continued problems in the eurozone, and UK dependence on these markets, was one reason why the US economy was growing faster than that of the UK.

France goes to the polls next Sunday to decide whether to elect the Socialist François Hollande, the favourite after the first round eight days ago. He has called for a renegotiation of the European fiscal pact to put more emphasis on growth.

Next Sunday, too, votes for the Greek parliament could lead to the election of a bloc opposed to austerity measures regarded as necessary to secure bailout funds. And Dutch elections have been called for September after Mark Rutte's government was unable to win support for an austerity package.

Merkel has insisted the fiscal pact is not up for discussion. She said last week: "The fiscal pact has been negotiated, it has been signed by 25 heads of government. It is already ratified by Portugal and Greece. It is not renegotiable."

Cameron believes it is the political stalemate in Europe – particularly about the role of the European Central Bank in managing the European economy – that is holding back growth in the UK. In a major speech at Davos last year, he argued that a system of fiscal integration and risk-sharing, perhaps by creating euro-area bonds, as well as structural reforms, was necessary for the euro to thrive. His remarks on Sunday suggest he does not believe the issues of competitiveness and governance have been resolved.

Ed Balls, the shadow chancellor, said: "It is no good the prime minister telling us that the eurozone crisis is going to last a long time. Cameron and George Osborne must accept their share of the blame."

A Sunday Times YouGov poll showed that 32% blame the return to recession on UK government policies, 29% on the eurozone and global factors, and only 17% on the last Labour government.

Cameron also insisted the UK needed to take further measures to make the economy more competitive. He listed the key issues as "how we get our banks lending, how we make sure the money goes into infrastructure, how we make it easier for businesses to employ people, how we boost our exports, how we make sure that manufacturing and the rebalancing in our economy takes place", adding: "All of those things are on the table."

He said his working day was full of meetings trying to ensure the government was implementing the growth programmes it had already set out. Government sources said ministers were looking hard at the welfare budget and Iain Duncan Smith, the work and pensions secretary, had highlighted plans to cut the government housing benefit bill by putting pressure on rents.