Twenty-one percent of the respondents said they did not know if it was necessary to hold a parliamentary vote on whether London should engage in the military actions against Syria.
The last time there were reports of chemical weapons being used in Syria by President Assad's government, President Trump launched a missile attack on a Syrian air base.
Conservative former London mayoral candidate Zac Goldsmith tweeted: "We need a clear response to the Syrian chemical outrage".
Some MPs have backed Britain acting against Syria, warning that the use of chemical weapons was in breach of global law and could not be allowed to go unpunished.
"They agreed to keep working closely together on the worldwide response", the statement concluded. The statement made no specific reference to military action.More news: Russian ambassador warns of 'consequences' after airstrikes in Syria
She continued: "The use of chemical weapons can not go unchallenged".
Russian Federation has said that it will respond to an attack using any means necessary, and will shoot any missiles down.
"While I realise that working for the "national interest" is an alien concept to Mrs May and our political establishment, they nevertheless should not be dragged into a war on the say so of Donald Trump or anyone else".
"Britain should press for an independent United Nations -led investigation of last weekend's horrific chemical weapons attack so that those responsible can be held to account".
Opposition Liberal Democrat leader Vince Cable told the BBC that parliament "can and should be recalled immediately" to hold a vote on the latest possible action.More news: Mets catcher Kevin Plawecki diagnosed with broken hand
A separate YouGov survey on Thursday found 61 percent of people think it would be necessary for parliament to vote on military action against Syria, with just 18 percent saying it was not necessary and 21 percent undecided.
May is not obliged to win parliament's approval, but a non-binding constitutional convention to do so has been established since a 2003 vote on joining the US -led invasion of Iraq.
So far, the United Kingdom has been launching air strikes in Syria from its military base in Cyprus, but only against targets linked to the Islamic State terrorist group.
May isn't legally required to get Parliament's backing for military action, though it is conventional for lawmakers to be given the chance to vote. That then deterred the USA administration of Barack Obama from similar action.More news: Defiant no further, Arizona governor bends to teacher requires