But on Thursday many trapped Britons and their families remained in the dark with no further information on when they would be permitted to leave.
Zaynab Wandawi, 29, a British teacher, went to Gaza with her husband and eight of her in-laws for a wedding two days before Hamas’s attack on Israel sparked the current war.
On Thursday, her mother Lalah Ali Faten accused ministers of failing to demonstrate their commitment to assisting British citizens.
Speaking to the Telegraph, Ms Faten said: ‘‘Yesterday we were hopeful that today would be the day that they would be able to leave.
“I didn’t sleep until about 2.30 then I woke up again at 5.30 and I saw that the list was already live,” she added.
“When I saw they weren’t on the list again I was desperately upset – I really do feel that the Foreign Office could have done more.”
The newly released list compiled by the Palestinian General Authority for Crossing and Borders includes the names of almost 600 foreign nationals cleared to enter Egypt.
Most of the people on the list, exactly 400, are US nationals.
‘Terrified and disenchanted’
However, there are hopes more British citizens could make it out and into Egypt on Thursday, after around 200 registered in Gaza with the Foreign Office.
Responding to the Prime Minister’s comments on Wednesday, Ms Faten said: “If getting British citizens home really was a priority for Rishi then the results would have been forthcoming.”
As of Thursday morning, Ms Faten had been unable to speak to her daughter and extended family.
Stella Creasy is one of several MPs assisting constituents with stranded relatives.
The Labour MP told the Telegraph: “The Government needs to be clearer with people who are waiting to leave about when they will be able to do so, otherwise they are just prompting people to make a perilous journey only to be turned away again.”
“These people are terrified and increasingly disenchanted,” she said.
The Telegraph has approached the Foreign Office for comment.