Americans and Britons are deeply sceptical about the idea of arming Syria's rebels and the possibility of sending western troops into the country, according to a bilateral poll.

Despite the escalating civil war, growing casualty figures and a rising tide of refugees flooding out of Syria, there is little appetite for more robust action than the current approach of providing "non-lethal support" to the rebels, the YouGov poll found.

There have been increasing demands on Capitol Hill to arm the opponents of the Assad regime or intervene more directly, and this week Barack Obama toughened his own rhetoric amid contested claims about Damascus using chemical weapons. But the new binational survey – produced for YouGov-Cambridge, the polling company's academic thinktank – finds US voters opposed to the idea of supplying munitions by a 29-point margin: 45% against to 16% in favour.

Identical questions were posed in Britain, where David Cameron has, with the French president, François Hollande, recently tried and failed to persuade the EU to lift its arms embargo. But the British public emerges as even more strongly against: 57% oppose arming the rebels and 16% are in favour.

In both the UK and the US, opposition to arming the rebels is marked on the right as well as the left of the political spectrum: 52% of American Republicans and 63% of British Conservatives are against supplying arms.

Any thought of sending western troops into Syria would also be badly received – especially in the UK. By a 32-point margin (55%-23%) Britons reject the idea of sending in UK and allied troops to protect civilians. The anti-intervention lead rises to 59 points (68%-9%) if the aim were "overthrowing President Bashar al-Assad".

In the US too, proposals to put boots on the ground would run up against public opinion. Americans lean 33%-27% against sending in troops "to protect civilians", and are more decisively against directly enforcing regime change, splitting 42%-16% against. Although more Republicans (22%) than Democrats (14%) would be prepared to support the latter, the partisan difference are not as great might have expected given the continuing divisions over the war to topple Saddam Hussein.

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A decade on from the invasion of 2003, YouGov reaffirms the verdict of other pollsters and finds a rough two-to-one (53%-27%) balance of Britons saying that the war launched by George Bush and Tony Blair was wrong rather than right.

US opinion is more evenly divided, with those who believe the war was right holding a slim 41%-38% edge. And whereas in Britain, opposition is consistent across supporters of different parties, in the US the political divide is stark. Democrats judge the war a mistake by a 53%-23% margin, but Republicans remain even more convinced that it was right, splitting 72% to 12% in favour.

While no political faction in either Britain or the US is comparably belligerent in connection with Syria, the mood is not isolationist either. There are strong majorities in favour of the official policy on both sides of the Atlantic, of providing the rebels with "non-lethal support".

In the US the Obama administration has concentrated on softer support, such as food and medical supplies, but the question's wording also referred to "armoured vehicles and body armour", the sort of harder-edged interpretation of "non-lethal" supplies being emphasised by London.

Even with the proposition put in these terms, Americans split 45%-24% in favour of providing the supplies, a 21-point margin. In Britain, the 57%-22% pro-intervention majority on this count is even more emphatic, at 35 points.

For pro-intervention hawks, such as Senator John McCain in the US and increasingly Cameron himself in Britain, there is another encouraging finding. Respondents on both sides of the Atlantic are in favour of "enforcing a no-fly zone over Syria so the Syrian air force cannot attack rebels or civilians". In the UK that proposition wins public support by a 43-point margin, with 61% in favour and 18% against. In the US there is a 50% to 18% majority behind the same proposition.

If these results point to mixed public attitudes to Syria, YouGov-Cambridge's detailed analysis on the legacy of Iraq also defies easy characterisation.

Britons are disinclined to believe the conflict made the world a safer place – only 14% say so, as against 38% who judge it has made the world more dangerous and 40% who say it made little difference. They are likewise disinclined to believe the invasion made the lives of ordinary Iraqis better (only 24% think so), and by 71% to 12% they also believe Iraq will remain "permanently unstable" as opposed to becoming a "peaceful democracy". Americans are somewhat more sanguine on all these counts, in line with their less hostile overall verdict on the war, but in the United States, too, a clear majority of 56% believes Iraq is set for permanent instability.

When memories of Saddam Hussein are invoked, however, the picture changes: by 41% to 21% Britons judge that despite the suffering of war Iraqis would have been even worse off under the rule of Saddam, and in the US opinion leans the same way, by 46% to 17%. These final results seem out of kilter with the UK's anti-war sentiment in particular. It could be that some respondents are reasoning that while Iraqi life would have been worse under Saddam he might by now have been brought down by other means – or it could be that people give different answers to similar questions phrased in different ways.

YouGov-Cambridge surveyed 1,684 British adults online on 10 and 11 March and a further 1,962 on 13 and 14 March, and 1,022 American adults online from 12 to 14 March. The figures have been weighted and are representative of British and American adults aged 18 or over.