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.
A spokesperson for the Foreign, Commonwealth and Development Office (FCDO) said: “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.
“We are regularly updating all British nationals registered us.
“The crossing will be open for controlled and time-limited periods to allow specific groups of foreign nationals and the seriously wounded to leave.
“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.”
It comes after Britons who attempted to make the crossing were turned back, despite hundreds of other foreign passport holders being allowed to cross.
Earlier on Tuesday, Foreign Secretary James Cleverly promised that UK teams would be ready to assist British nationals who are able to make the crossing.
Mr Cleverly said: “UK teams are ready to assist British nationals as soon as they are able to leave.
“It’s vital that lifesaving humanitarian aid can enter Gaza as quickly as possible.”
The border is expected to be open for time-limited periods under strict controls to allow specific groups of foreign nationals and the seriously wounded to leave.
The list of those allowed out has been agreed between Egypt and Israel, with the embassies from the relevant countries informed in advance.
The UK has a Border Force team in Cairo, with consular officials in Arish, near Rafah, to provide support for Britons who leave Gaza.
As Tel Aviv’s forces stepped up operations against the Hamas group, which carried out the October 7 atrocities in Israel, Mr Cleverly also stressed the need for humanitarian aid to get into Gaza.
Meanwhile, Deputy 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.
Asked by Sky News whether Israel has broken international law with the strikes, he said: “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 amongst the civilian population. This is a very difficult conflict.
“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 targeted Jabalia again on Wednesday.
The Palestinian death toll in the Israel-Hamas war has reached 8,525, according to the Hamas-run health ministry in Gaza. In the occupied West Bank, more than 122 Palestinians have been killed in violence and Israeli raids.
Labour called for the Disasters Emergency Committee (DEC) 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.
Mr Lammy said: “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.
“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.”