British Prime Minister David Cameron's failure to win parliamentary backing for military action against Syria has hurt him politically, polls showed on Monday, with most Britons thinking him "reckless" and support for his party falling.

A Comres/ITV poll showed that 59 percent of those asked thought he had been reckless to organise last Thursday's vote on military action without knowing whether he had lawmakers' backing.

Another poll showed the opposition Labour party had increased its lead over Cameron's ruling Conservatives to 10 from four percentage points after the parliamentary defeat, setting back his hopes of being re-elected in 2015.

"The 10-point lead is larger than we have seen of late, suggesting at least some impact from the Syria vote," YouGov, the second poll's organiser, said on Monday.

Britain's lower house of parliament voted against Cameron's Syrian plans by 285 to 272 votes on Thursday, inflicting a shock defeat on him even though he had already made big concessions to try to win approval.

It had long been clear that most Britons opposed their country being involved in military action against Syria and did not agree with Cameron, but Monday's polls suggest they think he badly mismanaged the overall situation too.

Cameron's office has ruled out a re-run of the Syria vote despite pressure from some senior lawmakers to do so, saying that "parliament has spoken" with ministers keen to blame Labour for sabotaging the vote, an accusation Labour dismisses.

Commentators say both parties want to avoid a repeat. In Cameron's case, losing another vote on Syria could trigger a leadership challenge against him, something that a significant minority in his fractious party would welcome.

Many politicians and commentators have also expressed fears that Cameron's defeat could damage Britain's 'special relationship' with the United States given that President Barack Obama had asked for and not got British military support.

However, another poll showed most Britons did not share that fear. The survey, by the BBC, showed that 72 percent of those asked did not think UK-U.S. ties would be harmed, and two thirds of respondents would not care if they were.