Voters back the police rather than David Cameron over the handling of riots, according to a Guardian/ICM poll. It shows that under a third of voters think the prime minister has done a good job – while overall trust in the police's fairness remains strong.

The poll, carried out online this week as politicians and the police became increasingly critical of each other's performance, suggests neither Cameron nor the mayor of London, Boris Johnson, have impressed the public with their response.

Only 30% say Cameron has done a good job, against 44% who say the opposite, a net negative score of -14. For Johnson, the figures are 28% good job and 38% bad, a negative of -10 points. By contrast, 45% think that the acting commissioner of the Metropolitan police, Tim Godwin, has done well against 27% who say the opposite – a positive score of 18.

Another online poll, conducted this week by YouGov, found similar levels of support for the police response over that of politicians. There is some evidence – on a smaller and therefore less precise sub-sample – that Londoners judge Johnson less harshly than the rest of the country. In the capital, his net negative score is only -3.

Guardian/ICM poll on the England riots. Photograph: Guardian

Despite the scale of the rioting, and accusations that the police mishandled the initial disorder in Tottenham, public trust in the police seems uniformly strong. Overall 61% of those polled say they are confident that the police enforce the law fairly, uniformly and without prejudice.

By contrast a total of 36% say they are either not at all (10%) or not very (26%) confident. There is some evidence that younger or poorer people are less likely to trust the police than older or better-off ones, but in all categories a majority are satisfied.

However, the public are far less confident about the police's ability to keep order. A majority say they think the police lack sufficient resources. The finding could add to opposition to cuts in police numbers and funding.

In the Commons on Thursday, Cameron came under fire from the Labour leader, Ed Miliband, and some backbenchers over plans for cuts and the head of the Association of Chief Police offciers (Acpo), Sir Hugh Orde, has warned they will restrict the police's ability to respond to disorder.

While 41% say they are either very (6%) or quite (35%) confident the police have been given adequate resources, 56% say the opposite. People on lower incomes are the most likely to think the police are under-resourced.

There is also widespread agreement about the main causes of the riots and looting.

Asked to pick from a list of possible reasons, 45% blame criminality on the part of the rioters. Older voters and richer ones are most likely to lay the blame on this.

Of other possible reasons, 28% cite lack of respect within families and communities. Only 8% think a lack of jobs for young people is the main reason. A further 5% say the shooting by the police of Mark Duggan, which led to the initial disorder in Tottenham, was the main cause, while 4% blame the coalition government, 2% the police and 2% the state of the economy.

At the bottom of the list only 1% blame racial tension – a finding that suggests these riots are being seen differently by the public to those of the 1980s.

• ICM Research interviewed a sample of 2,008 adults aged 18+ online on 10-11th August 2011. Interviews were conducted around the country and the results have been weighted to the profile of all adults. ICM is a member of the British Polling Council and abides by its rules.