You would not know it from most news reports, but David Cameron's weekend admission that Britain will not be sending arms to Syria's rebels masks a major political defeat. The prime minister gave no reason, but it's clear he has been forced into a U-turn by a large backbench revolt, including many from his own party.

A backbench-promoted debate that prominently featured the tenacious John Baron (one of the 15 Tory MPs who voted against the Iraq war) and Peter Hain, a former Labour minister who once handled Middle Eastern issues, ended with a stunning rebuke to the government. By a margin of 114 to one, they demanded that the government put the issue to a Commons vote before sending any arms. William Hague was forced to promise this would be done.

This rare backbench victory should be celebrated. Seeing the chaos of post-Gaddafi Libya, many MPs were stung by the fact that Britain took military action there in 2011 without coming to parliament first. Others were guided by the bitter experience of the Iraq war. They know now that, although prior consent was sought and obtained from MPs on Iraq in March 2003, it was achieved on the basis of false evidence and "sexed-up" intelligence.

But it was not just the issue of prior consent that underlaid the recent Commons vote on Syria. Most of the 114 who challenged the government are against arming the rebels on principle, for fear of launching a new arms race that would increase the killing in Syria, or because they fear British weapons would end up in jihadi hands.

In taking this view backbenchers are following the instincts of the majority of British citizens. A recent Opinium/Observer poll found that only 24% supported giving weapons or military supplies to Syria's rebels. Britons have learnt the lesson of the disastrous British interventions in Iraq and Afghanistan. The same poll found that about 60% now oppose both wars.

The Labour frontbench is gradually learning the lesson too. On Afghanistan it still goes along with the government's view (at least the view that ministers express in public) that Britain's military involvement has been worthwhile and a success, no doubt so as not to add further distress to the families of all the British troops whose lives were cut short in a hopeless venture there. But on Syria Douglas Alexander, the shadow foreign secretary, is firmly against sending British weapons into the sectarian conflict. With Labour and the Lib Dems ranged against Cameron's wishes, as well as so many Tory backbenchers, the whips have told the prime minister this policy will never pass.

This is all the more welcome since it runs against the mood in Washington, which British ministers and would-be ministers often follow. US public opinion is firmly against arming Syria's rebels – a Huffington Post/YouGov poll last month found only 19% in favour of sending them weapons, while 53% were against. Even though a narrow majority of Americans believe Syrian forces have used chemical weapons in the conflict, most of this group is still opposed to sending weapons to the other side. Two other US polls had similar findings.

The Obama administration seems determined to ignore the American people's views. It has been lobbying hard to convince Congress to support the plan to give the rebels US weapons. After briefings in closed sessions, the intelligence committees of both houses have just approved it, though it is still not clear when the arms will actually be sent.

The best way to pressurise for an end to the Syrian war is to do precisely the opposite of adding more weapons. Instead, urge Russia and Iran to suspend their arms supplies unless and until President Assad's ministers come to the promised Geneva conference with convincing proposals for a government of national unity. For its part, the west should cut the training and other so-called non-lethal help that it already gives the rebels, unless and until they agree on sending a credible delegation to Geneva that would be willing to discuss local ceasefires and a transition to an inclusive Syrian administration that would protect minorities and reduce sectarianism. Negotiations on these lines will be hard, and perhaps it is already too late, but sending more weapons is infinitely worse.