David Cameron's personal popularity has dropped, and the Liberal Democrats' poll rating has hit its lowest level for 14 years, a Guardian/ICM survey has revealed.

But while the poll offers no joy for the coalition, it gives scant comfort for Labour: the party retains a narrow lead among voters in a hypothetical general election, but Ed Miliband's personal rating has slumped again and he is now competing with Nick Clegg for the title of most unpopular leader.

Overall, hostility to the coalition has grown sharply, with 50% of voters saying the government is doing a bad job and only 35% saying it is doing a good job – a net rating of -15%. That is 10 points worse than March and 38 down on June last year, when the coalition was enjoying a honeymoon.

The poll was carried out at the weekend after a difficult few days for the coalition, dominated by the relaunch of the NHS plans and announcements of industrial action by several public sector unions.

Cameron remains more popular than either his party or the coalition, but only just, and he is in negative territory for the first time. While 42% say he is doing a good job, 47% say bad, a score of -5. In March his score was +5 and last June it was +23.

Scores for the chancellor, George Osborne, and Clegg are even worse. Osborne has a net negative of -12, compared with -2 in March. The deputy prime minister has fallen less fast, but only because he was already at rock bottom. His score is -20%, down two on March, with 54% saying he is doing a bad job, including 55% of people who voted Lib Dem in the general election.

Labour is on 39%, up two on last month, and the Conservatives on 37%, up one. The figures for the two main parties are the same as last December, and there has been little significant variation since then.

But the Lib Dems have dropped three points in a month, to 12%. That is as low as the party has scored in an ICM poll since September 1997, in the aftermath of Tony Blair's first election victory.

There is some sign that the Green party, on 3%, is picking up votes along with the other smaller parties, who polled a combined score of 12%, up one.

Only 28% of all voters, and just 45% of Labour supporters, think Miliband is doing a good job. His net negative is -21, down eight points since March. His rating is one point worse than Clegg's and 16 points worse than Cameron's. The Labour leader seems notably unpopular among older voters and men. His popularity ratings now resemble those of Iain Duncan Smith when he was leader of the opposition, and Miliband's rating is notably worse than those of William Hague or Michael Howard as opposition leaders.

There is only slightly more cheer for Labour in public attitudes to policies. Forty-nine per cent of voters back coalition plans to raise the pension age for public sector works from 60 to 66, with 41% opposing them. A differently worded online poll at the weekend found stronger opposition, but the results suggest unions should not rely on public backing for strikes.

The government will also be pleased by its 12-point lead on the economy, arguably the most significant policy area. While 40% think the coalition's policies are best, only 28% back Labour – well below the party's actual level of support. Men are keener on the coalition's economics than women. Even so, there is little perception of an economic recovery. Fifty-three per cent say they are not confident about their financial circumstances, against 46% who are, a net negative of -7, only slightly better than -13 in March. Tory voters are twice as confident as Labour ones.

Attitudes to other policy areas break along party lines. Labour leads on health and education, but not by as much as the party might hope given the rows over the government's NHS and school plans.

On health, the coalition is backed by 31% – combining Tory and Lib Dem supporters as would not happen at a general election – while Labour is backed by 38%, a seven point lead. On education, the picture is similar: 31% for the coalition, 36% for Labour, a five-point Labour lead.

But on the broader issue of taxation and public services, the coalition leads by two points, 35% to 33%. On law and order, despite the tabloid row over Kenneth Clarke's sentencing plans, the lead is 13 points, 36% to 23%. On immigration it is 16 points, 36% to 20%. On Europe, 10 points, 30% to 20% in favour of the coalition.

• ICM Research interviewed a random sample of 1,000 adults aged 18+ by telephone on 17-19 June. Interviews were conducted across the country and the results have been weighted to the profile of all adults.