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In total, 260 lawyers have signed the letter to call on Mr Sunak, Foreign Secretary James Cleverly and Defence Secretary Grant Shapps to "act urgently" so the UK can "fulfil its international legal obligations" in the conflict.
Signatories include 36 King's Counsel, 49 partners and directors of law firms and 16 law professors.
In the letter, they urge the government to stop the sale of arms to Israel because they may be used in “serious violations” of international humanitarian law.
The lawyers also call on the government to "exert its influence to press for a ceasefire to allow aid into Gaza".
Israel, which is preparing to launch a ground invasion to the Palestinian enclave, has struck the strip repeatedly from the air following Hamas's surprise attack on October 7, which killed at least 1,400 people, mostly civilians.
More than 7,000 people in Gaza have since been killed in retaliatory strikes, its Health Ministry said.
"We are moved to intervene because, in a region already accustomed to great suffering, the death and other harm visited on individuals, families and whole communities in the last 20 days has been truly terrible," the letter said.
"The starvation of a civilian population as a method of warfare, including wilfully impeding adequate relief supplies, as Israel is doing in Gaza, is strictly prohibited under customary international law ... and constitutes a war crime.
"Hamas's war crimes cannot be justified by reference to prior war crimes by Israel; neither do they justify further such crimes by Israel in its response, which must comply with international law."
The letter also says that, according to international law, the UK must not encourage, aid or assist others in breaching the law.
The latest from the Israel-Gaza war - in pictures
It comes after EU leaders called for "continued, rapid, safe and unhindered humanitarian access and aid to reach those in need".
Mr Sunak said on Thursday that he was pushing for a pause in the fighting between Israel and militants to allow aid to reach Palestinians and also create a "safer environment" for UK citizens to leave the besieged enclave.
Leader of the opposition Labour Party, Keir Starmer, has also backed calls for a humanitarian pause, as opposed to a full ceasefire, which the government has said would benefit Hamas.
But many members of Mr Starmer’s party have urged him to go further, with about a quarter of Labour MPs, including two front-benchers, publicly calling for a ceasefire.
On Friday, the Education Secretary said ministers are continuing to resist calls for a ceasefire in the Middle East, but the UK is "reliant on" a humanitarian pause in the conflict to get support into the region.
Gillian Keegan said the government needs to "ensure" that there is a break in fighting in order to get aid into Gaza and allow British citizens to leave the bombarded 25-mile strip.
Asked why ministers would not call for a cessation of violence, Ms Keegan told ITV's Good Morning Britain that the Government would not want to "cross that line of telling Israel it has anything but the right to defend itself".
"Hamas have created this situation and Hamas are now embedding themselves in the Palestinian population," she said.
She said that facilitating any humanitarian pause would in itself be "very difficult" and the UK would be "reliant on" it being observed.
"It's operationally very difficult and that's why we've sent a plane-load of aid, it's why we've sent Border Force, it's why we've got people there, our International Development Secretary has been working with a lot of people in the region to make sure that we're prepared to be able to get this aid to the right place," she said.
The Foreign Office has said it was in contact with about 200 UK citizens in Gaza.
"We're very keen to be able to bring them out and bring them home," Mr Sunak said.
"What I can tell you is we've pre-positioned Border Force teams to Egypt. So that if there is a possibility for our nationals to cross the Rafah crossing, we're ready to get them in and bring them back."
The lawyers who signed the letter include former chairman of the General Council of the Bar of Northern Ireland, Brian Fee, former chairman of the Criminal Bar Association of England and Wales, Andrew Hall, and former Counsel General for Wales, Theodore Huckle.