More British citizens have begun to leave Gaza, after Palestinian authorities listed nearly 100 as being eligible to cross to Egypt on Friday.
The UK section of the Palestinian border authority list names more than 90 people as British nationals.
The parents-in-law of Scottish First Minister Humza Yousaf, trapped in Gaza since 7 October, have left.
But the OceanNewsUK is aware of at least 19 people named on the list who are unable to leave via the Rafah crossing.
Three family groups have said they are located in the north of Gaza but it is too dangerous to travel to the south where the crossing is located.
About 200 British nationals are believed to be in Gaza.
A small number have already left after some foreign nationals and injured Palestinian people began to be allowed to go through the crossing into Egypt for the first time from Wednesday.
Border crossings in and out of Gaza have been closed since 7 October, when Hamas, which is a proscribed terrorist organisation in the UK, attacked Israel, killing more than 1,400 people and taking more than 240 hostage.
Since then, the Israeli military has launched a massive bombing campaign on Gaza, placed the strip under a "complete siege" and recently launched a ground assault on the north of Gaza. The Hamas-run health ministry in Gaza says more than 9,000 people have been killed.
The UK section of the list published by Palestinian authorities contains 127 names, with 92 listed as being British nationals. But it is not clear if the others, the vast majority of whom are described as Palestinian, also hold dual citizenship.
Mr Yousaf's parents-in-law Elizabeth and Maged El-Nakla, who live in Dundee, were among those on the list and waiting to leave Gaza after being trapped there while visiting relatives before the borders closed.
In a statement on Friday, the first minister and his wife Nadia confirmed her parents have left Gaza, but did not specify if they have made it to Egypt.
The couple expressed gratitude to people who have "assisted our parents over the last few weeks", including the Foreign Office crisis team.
"These last four weeks have been a living nightmare for our family, we are so thankful for all of the messages of comfort and prayers that we have received from across the world, and indeed from across the political spectrum in Scotland and the UK," they said.
Speaking on Friday security minister Tom Tugendhat said the British government was being "very cautious" about giving an exact number of people who will be able to get out because "we neither control the border, nor do we control what's going on inside Gaza".
"So what we don't want to do is give false hope or false belief to individuals that they'll be able to cross today," he told OceanNewsUK.
Mr Tugendhat said there was a list of people who have been approved to cross out of Gaza as soon as possible, as agreed by the Egyptian and Israeli governments.
In terms of British nationals, he said the list has been validated by the UK government to include British citizens, or dependent or entitled people.
The UK has deployed a Border Force team in Cairo, as well as consular officials in Arish, near Rafah, to provide support for UK nationals after leaving Gaza.
Surgeon Abdel Hammad, who lives in Liverpool, was among those who were able to exit via the Rafah crossing into Egypt on Thursday, his family have said.
Downing Street previously confirmed that two UK aid workers were among those to make it through Rafah, which is the only Gazan border crossing not controlled by Israel.
On Thursday, the Foreign Office said more British nationals had managed to pass through the Gaza-Egypt border, but did not confirm how many.
A dual UK-US citizen who left Gaza on Thursday with her family has told the OceanNewsUK an exception was made for her British-Palestinian husband at the border as he was with family on the list of US citizens eligible to leave.
Dr Emilee Rauschenberger, an academic who lives in Salford, described the situation at Rafah as chaotic, with many people struggling to make it to the far-south of Gaza without cars or access to other transport.
She told OceanNewsUK's Today programme on Friday there was no system to divide people who were eligible to leave and those not on a list but hoping to cross, creating a stressful situation.
After waiting many hours on the Gazan side of the border crossing, the family made it through to Egypt where they were given food and water and seen by medical staff.
Dr Rauschenberger said British embassy staff in Egypt told her about 10 British citizens, who she believes work for aid agencies or other international organisations, also crossed on Thursday.
The UK government has given both the Israeli and Egyptian authorities a list of British citizens and their dependants, prioritised by their medical vulnerability.
Dr Ahmed Abou Foul, who is based in Birmingham, has told the OceanNewsUK that 16 members of his family who are trying to leave Gaza are on the list, including eight children.
He says he has mixed feelings about the news because two young children and their mothers, his sisters-in-law, will not be be able to leave as their names are not on the list.
Dr Abou Foul told OceanNewsUK on Friday the family do not know why they have been excluded, as he said they had been given assurances from the Foreign Office.
