Two Conservative MPs have written to the Government expressing their concern over the situation in Gaza as a veteran Liberal Democrat called on the Prime Minister to recall Parliament.
In a letter to Foreign Secretary Philip Hammond, Margot James (Stourbridge), who is now working with William Hague, said her constituents regarded the Israeli action as "wholly disproportionate to the threat posed by Hamas".
The correspondence, seen by Channel 4 News, went on: " 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.
"I also think that we should make it clear that it is unacceptable for Israel to just dismiss US proposals for peace without any debate whatsoever."
Fellow Tory Sir Peter Bottomley, who has emailed the chief whip Michael Gove, told BBC News that Israel must find that world opinion would not tolerate "this degree of death and devastation".
The MP for Worthing West, who has also sent a letter to the Israeli ambassador, added: "The issue now is if Israel is relying on other people to be silent, they will go on with the lack of proportionality and the death.
"Anyone who looks at the pictures of what is going on presently in Gaza...must know that the Israelis know what they are doing and what they are doing is wrong. Many Israelis know it is wrong."
He said the vast majority of Conservative MPs wanted to see Israel's right to exist recognised but did not believe the level of aggression shown was justified.
Meanwhile Sir Bob Russell, who sits on the defence committee, has called for an emergency session of the House of Commons as the civilian death toll continues to rise.
In a letter to David Cameron, he wrote: " On Monday last week...I suggested to you that the disproportionate action of Israel's political and military leaders constituted war crimes.
"In response you said that 'international law' required Israel to defend itself in a 'proportionate way'.
"Since I put this matter to you, more than a further 1,000 Palestinians - mostly civilians, including hundreds of children - have been killed by military attacks by Israel.
"If you, as Prime Minister, had ordered British troops to fire on civilian communities in the way Israelis have then you would be guilty of a war crime.
"As it is clear that Israel's behaviour is not proportionate, and that by their deliberate actions this places Israel's political and military leaders firmly in the court of international law to face war crimes, I write to request please that you arrange for the recall of Parliament in the coming week to debate the deteriorating situation in Gaza."
In a separate statement, shadow foreign secretary Douglas Alexander said the killing of sleeping Palestinian children taking shelter in a school bus had "horrified even those hardened to sustained suffering".
He added: "The reaction of people across the world to these scenes of bloodshed is to ask how many more children will die before a cessation of violence is achieved.
"Indeed 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.
"Labour opposes the Israeli incursion into Gaza and reiterates its call for a ceasefire to now be agreed, to secure an end to the bloodshed and suffering and to allow dialogue, in time, to replace violence."
In his email to the chief whip, Sir Peter wrote: "We each know Israel has the right to exist. We know and ask that the attacks on Israelis cease. We know the settlements outside the proper borders of Israel are wrong.
"The situation now is different. That is why I have written this serious letter to Daniel Taub [Israeli ambassador]
"His Government has to pay attention to informed opinion amongst those who are not prejudiced against them."
In the letter to Mr Taub, he asked: "How many people in Gaza had electricity last week? How many will have electricity next week?
"Why do Israeli military spray sewage on shop fronts? Is it policy to refer to Palestinians as Arabs?
"Why does Israel appear to value differently the lives of Israelis and Palestinians?"
A Foreign Office spokeswoman said the UK was "deeply concerned" about the situation in Gaza and the tragic loss of life on all sides.
She added: "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.
"After a ceasefire has been agreed, we can then move to more substantive discussions on the underlying issues, including Israeli restrictions on Gaza, the conditions in Gaza and the threats to Israel from rockets and tunnels.
"Israel has the right to defend itself, but must do so in a way that complies with international law - in particular the principles of proportionality and necessity - in order to minimise the loss of civilian life.
"We remain focused on these priorities: securing a ceasefire, alleviating the humanitarian suffering, and keeping alive the prospects for peace negotiations, which are the only hope of breaking this cycle of violence."
Former Foreign Office minister Alistair Burt said the first step had to be securing an unconditional ceasefire.
He told Channel 4 News: "The most important thing is to stop the fighting and then get the talking started.
"We have to see how complex this is and what needs to be done. It is not just talking to Israel about what they should or shouldn't do.
"Israel will say well you are talking to us, no-one has talked to the Syrian Government about what they do...no-one talks to Hamas.
"The truth is this won't be settled until Arab states are able to pull Hamas away from Israel and their refusal to accept the existence of Israel.
"Let us get to Israel and say there is no answer to this unless they fully conclude the settlement with the Palestinian authority, those who have been willing to work with Israel, and don't fight it."
Asked about the White House's condemnation of the deadly school shelling on Wednesday, he said it was "genuinely remarkable".
US spokeswoman Bernadette Meehan said earlier the Obama administration was "extremely concerned" that thousands of Palestinians were not safe in UN-designated shelters.
But Mr Burt insisted he did not have concerns about the British Government's policy.
Asked why it could not follow America's lead, the Tory MP for north-east Bedfordshire replied: "I'm not speaking for the British Government."
Questioned on whether it was time for Britain to use its influence to help bring about a solution, Mr Burt said: " From what I understand the Foreign Office is using every bit of leverage it can."