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Prime Minister Rishi Sunak has vowed to continue working closely with Egypt and Israel to ensure more British citizens can leave Gaza safely.
It comes as the first Britons were able to leave Gaza via the Rafah border crossing into Egypt on Wednesday night.
About 200 British citizens have registered in Gaza with the Foreign Office.
Officials said the crossing will be open for “controlled and time-limited periods” to allow specific groups of foreign nationals and the seriously injured to leave Gaza.
The Foreign, Commonwealth and Development Office said it has agreed, with Egyptian and Israeli authorities, a list of British nationals that want to leave Gaza.
“We will continue working with partners to ensure the crossing is opened again, allowing vital aid into Gaza and more British nationals to leave safely,” it said.
“We are regularly updating all British nationals registered with us.
“We have agreed a list of British nationals that want to leave Gaza with Egyptian and Israeli authorities.
“We will be informed in advance when those on the list can use the crossing to ensure we can provide assistance.”
In a call with Egypt's President Abdel Fattah El Sisi, Mr Sunak welcomed the opening of the crossing.
“The Prime Minister thanked President Sisi for his efforts and said the UK would continue to work closely with Egypt and Israel to ensure all British citizens can leave Gaza safely,” a Downing Street spokesman said.
“The leaders talked about urgent work to increase the flow of humanitarian aid into Gaza, and the Prime Minister updated on plans for a second UK aid flight to support the work of the Egyptian Red Crescent. He said ensuring life-saving aid and medical treatment reaches civilians by all available routes is a top priority and the UK stands ready to provide further support.
“The Prime Minister and President Sisi also discussed diplomatic efforts to secure the release of hostages held by Hamas, prevent escalation in the wider Middle East and achieve long-term peace and prosperity for the Palestinian people.”
British citizens who earlier tried to make the crossing were turned back, despite hundreds of other foreign passport holders being allowed to cross.
British teacher Zaynab Wandawi, 29, from Manchester, was turned away when she tried to cross the border.
She had travelled to Gaza at the beginning of October with her husband, who is British-Palestinian, and his relatives for a family member’s wedding before the war erupted.
Her mother, Lalah Ali-Faten, 52, said when the couple arrived at the border they were told their names were not on a list of people permitted to leave.
“They went to the border, they were denied exit, they were informed that British nationals are not leaving today and their names are not on the list,” she said.
“They’re waiting for names to be released so they can leave.
“They’re hoping it’s just a waiting game and they’ll get out as soon as possible but they went to the border, they queued up, they spoke to the officials and they said no British nationals are leaving today, (saying) ‘your names are not on the list’.
“It’s very frustrating when you hear that they are allowing foreign nationals to leave and then you have that surge of hope and then throughout the day when they tell you we’re not on the list, it’s really frustrating.
“It kind of gets me upset with the Foreign Office, to be honest. Why are they not prioritising their citizens when other countries have managed to do the same for theirs?”
Ireland’s Minister for Trade Promotion Dara Calleary said its Department of Foreign Affairs is “working incredibly hard” to get Irish passport-holders out of Gaza. It is understood to be helping 35 people.
On Tuesday, Foreign Secretary James Cleverly promised that UK teams would be ready to assist British citizens who can make the crossing.
“UK teams are ready to assist British nationals as soon as they are able to leave,” he said.
“It’s vital that life-saving humanitarian aid can enter Gaza as quickly as possible.”
The UK has a Border Force team in Cairo, with consular officials in Al Arish, near Rafah, to provide support for British citizens who leave Gaza.
Israel intensifies attack on Gaza – in pictures
As Israel’s forces increased operations against the Hamas group, which carried out the October 7 attacks, Mr Cleverly also stressed the need for humanitarian aid to get into Gaza.
Deputy British Prime Minister Oliver Dowden said Israel’s air strikes on the Jabalia refugee camp on Tuesday, targeting a Hamas commander, are part of the “terrible nature” of the conflict.
“Hamas is a terrorist organisation that has murdered in cold blood over 1,000 innocent Israeli men, women and children, and now seeks to hide among the civilian population. This is a very difficult conflict,” he said.
“We continue to urge the Israeli government to abide by international law. I believe that the Israeli government is continuing to do so against an enemy that hides among civilians.”
Israeli forces were reported to have struck Jabalia again on Wednesday.
More than 9,000 Palestinians have been killed, according to the Health Ministry in Gaza.
In the occupied West Bank, more than 122 Palestinians have been killed in violence and Israeli raids.
Britain's Labour Party called for the disasters emergency committee to set up an appeal for Gaza, matched by taxpayer funding.
Shadow foreign secretary David Lammy and shadow cabinet development minister Lisa Nandy were in Cairo for talks about the crisis.
“There is an urgent need to alleviate humanitarian suffering in Gaza and a DEC appeal with government backing would help galvanise the public’s efforts to help those in need,” Mr Lammy said.
“We must also begin to plan for the large-scale reconstruction that will be required for the people of Gaza to live in peace and dignity.
“In the long term, there can only be a political solution based on a two-state solution.”
