David Cameron and Ed Miliband have been urged by senior MPs within their own parties to demand more forcefully that Israel stops its bombardment of Gaza.

In a significant intervention, Margot James, a No 10 policy board adviser and parliamentary aide to William Hague, has written to the new foreign secretary, Philip Hammond, urging him to rethink the government's stance, calling Israel's actions disproportionate.

Stressing that she has been a firm supporter of Israel for many years, James wrote to Hammond: "I ask that the government rethinks policy towards the conflict in Israel and the Palestinian territories. The scale of suffering in Gaza is far too great, the loss of life, and particularly the lives of children and other vulnerable individuals, cannot be justified on the grounds of defence in proportion to the level of threat faced by Israel from Hamas."

So far, Cameron has stood up for Israel's right to defend itself and blamed Hamas for starting the conflict, while calling for an immediate ceasefire to end the bloodshed.

The former Northern Ireland minister Sir Peter Bottomley wrote to the chief whip, Michael Gove, criticising the "devastation and death" and arguing that most MPs in the centre of the Conservative party felt the same.

"We all know that Israel has the right to exist, we all know that the attacks on Israel should cease, we know that Israel's settlements and their treatment of Palestinians is provocative. That's the foundation. The issue now is if Israel is relying on other people to be silent, they'll go on with a lack of proportionality and the devastation and the death.

"Anyone who looks at the pictures of what's going on presently in Gaza must know that the Israelis know what they're doing and what they're doing is wrong," Bottomley told the BBC. "Many Israelis know it's wrong. [The prime minister Binyamin] Netanyahu may have support, but Israelis know that if you go killing people at this rate, the disregard for the life of Palestinians is going to show up in the world as a bad mark for Israel."

In contrast to the Conservatives, Labour opposes the invasion of Gaza.

Douglas Alexander, the shadow foreign secretary, said: "The growing number of Palestinian civilians being killed is rightly provoking international outrage, and the continuing incursion into Gaza risks further international isolation for Israel and further international condemnation of its actions."

However, Diane Abbott, a Labour MP and former shadow minister, said she would like to see Cameron, Miliband and the Liberal Democrat leader, Nick Clegg, do more to put pressure on the Israelis to stop the shelling.

"Leaders of all the parties need to be a great deal more emphatic in their condemnation of what's happening in Gaza," she told the Guardian. "Public opinion in all quarters, including Margot James who has always supported Israel, is horrified about what is happening. There is increasingly a consensus among ordinary people that they want to see the British political leadership speak out more emphatically. Part of it is people trying to keep in step with America, but things have gone so far, British leadership have to be prepared now to question America's support for what Israel is doing."

Several other senior Labour MPs had tweeted about the issue. Jon Trickett, a shadow cabinet office minister, wrote: "My mothers [sic] family were Jewish but what's happening in Palestine is #NotInMyName." Sadiq Khan, the shadow justice secretary, quoted the words of the UN's Ban Ki-moon, who said shelling of a school in Gaza was "Outrageous, unjustifiable and demands accountability and justice".

The US said on Thursday that casualties in Gaza were "too high" and Israel needed to do more to protect civilian life. However, the Foreign Office position remained the same. A spokesman said: "The UK is deeply concerned about the current situation in Gaza and the tragic loss of life on all sides. The foreign secretary has been absolutely clear that there needs to be an immediate and unconditional ceasefire to help alleviate the appalling humanitarian situation. All our efforts must be focused on achieving that ceasefire. Demands to take a different tack will simply dilute attempts to secure that."