The British public strongly supports tougher sentencing for those involved in rioting, a Guardian/ICM poll has found, with about 70% of respondents saying they thought people convicted of riot-related offences should get a tougher than normal sentence.

The severity of sentences has been the focus of much debate. Two men were jailed for four years after using Facebook in a failed attempt to incite a riot this month, and a woman was jailed for receiving stolen shorts during the disturbances but freed on appeal.

The poll also showed that support for the Conservatives remained steady at 37% in August – the same as July – with the party standing one point ahead of Labour. The Liberal Democrats were up one point at 17%.

David Cameron has championed severe punishment for rioters, telling the Commons that anyone convicted "should expect to go to jail". He threw his support behind the sentencing in the Facebook case, saying the court had decided "to send a tough message". "I think it's very good that courts are able to do that," he added.

The prime minister has faced criticism for this stance, with MPs, lawyers and campaigners warning against "disproportionate" sentencing.

The Guardian/ICM poll asked: "Do you think that people convicted of theft or other offences during the recent riots in London and elsewhere should or should not receive a tougher prison sentence than they might ordinarily expect, in order to set an example of them?"

Of the respondents, 70% said they believed offenders should receive a tougher sentence, while 25% believed they should not. Five per cent said they did not know.

The survey found that those who would vote Tory were more likely than Labour and Liberal Democrat voters to favour tougher action (82% versus 65% and 60% respectively), while tougher sentencing was also preferred by more women (74%) than men (66%).

The poll showed that those in the DE social group were far more likely to think rioters should receive tougher sentences than those in the higher income AB group. In the DE group, 80% of people believed those involved should receive harsher sentences, while in the AB group only 64% were of the same opinion.

Last week, the leading criminal barrister John Cooper QC warned that judges and magistrates had a duty "not to be influenced by angry Britain", describing some of the sentences handed down already as "disproportionate and somewhat hysterical".

Senior Liberal Democrats also urged caution, opening up a rift in the coalition. Lord Macdonald, the Liberal Democrat peer who led the Crown Prosecution Service in England and Wales for five years, warned that the courts risked being swept up in a "collective loss of proportion", passing jail terms that lack "humanity or justice".

His fellow peer Lord Carlile, the barrister who until this year was the government's independent adviser on terrorism strategy, warned against ministerial interference in the judicial process, arguing that "just filling up prisons" would not prevent problems.

The former Liberal Democrat leader Sir Menzies Campbell said it was important that political influence was not directed at the judicial system.

"With all due deference to the prime minister, politicians should not be either cheering or booing in the matter of sentencing," he said.

• ICM Research interviewed a random sample of 1,004 adults aged 18+ by telephone on 19-21 August 2011. Interviews were conducted across 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