Less than a quarter of the public believes that the government should arm the rebels in Syria, according to a poll in the wake of Britain's support for the lifting of an EU arms embargo.

Just 24% back giving weapons or military supplies to the forces fighting President Bashar al-Assad's army, although more than half (58%) would support offering humanitarian aid.

Last week the European Union lifted its arms embargo on Syria, with the foreign secretary, William Hague, claiming that the policy was denying rebels the right to defend themselves when they were "having every weapon that's ever been devised dropped on them". A number of European states, led by Austria, continued to oppose lifting the embargo, but Britain insisted that it should be allowed to expire on Friday. Hague, in a concerted move with France designed to force Assad to the negotiating table, said that the decision gave the UK and others flexibility in responding to a worsening situation.

An Opinium/Observer poll published on Saturday suggests that public opinion would not be behind any military intervention, no matter how hands-off. In a sign of the public's changing attitude towards Britain's role in the world, 78% of those polled said that they believe the UK is too overstretched as a result of Iraq and Afghanistan to intervene in a new conflict. Nearly three quarters (72%) believe that the UK can no longer afford to act as a major military power. More than two thirds (69%) believe that the UK should restrict the military to protecting UK territory and providing humanitarian aid in times of crisis.

Respondents broadly disapproved of the Iraq and Afghanistan conflicts with just under a third saying they supported them and around 60% opposing the interventions. Yesterday the United Nations said more than 1,000 people were killed in Iraq in May, the highest monthly death toll for years. Respondents were narrowly in favour of the no-fly zone in Libya, with 46% supporting it and 32% opposing it.

Britain and France's main aim has been to pressure Assad to make concessions at a peace conference proposed for later this month in Geneva. The threat is that weapons will be sent to the rebels if he is felt not to be negotiating in earnest.

The two allies believe the situation in Syria is growing worse daily and that arming pro–western rebels would make it less likely that international jihadists would take over the revolution. However, a group of five EU states, and many British MPs from both sides of the Commons, fear that arming the rebels will boost jihadists.

Douglas Alexander, the shadow foreign secretary, has also questioned the policy. "How would the government prevent British-supplied weapons falling into the wrong hands, and how does supplying weapons help to secure a lasting peace?" he asked.

Meanwhile, the US and Germany have called on Russia not to supply Syria's military with an advanced missile system after Assad said that a Russian contract to supply the S-300 surface-to-air missile defence system was being implemented, without confirming any deliveries.