A British-Palestinian group has written to Prime Minister Rishi Sunak, asking for an "urgent meeting" about Gaza.
The letter also urges the UK government to "use its influence" to call for a ceasefire.
It was sent, earlier on Monday, by the UK-based International Centre of Justice for Palestinians.
The ICJP said it was speaking "on behalf of members of the Palestinian community in the UK with families and loved ones living in Gaza".
The group said it wanted a meeting "to express our concerns, similar to the meetings you have had with other British communities who have families in the region who have experienced distress similar to ours".
Calls for humanitarian pauses were "inadequate", it said. And the government's failure to call for a ceasefire "is putting our loved ones in danger and is contributing to an unprecedented humanitarian crisis".
"It also ignores our voices as British citizens with friends and family under attack in Gaza," the ICJP said.
A spokesperson for the UK government told the BBC that it had "helped more than 150 British nationals and dependents to leave Gaza so far".
"We must see humanitarian pauses that allow enough time for hostages to be released, as well as aid to go in," it said.
It said the Foreign Office was in regular contact with those who remained in Gaza, "and our teams are working around the clock with the Israeli and Egyptian authorities to ensure they can leave as quickly as possible".
Six British-Palestinians told a press conference dozens of their family members had been killed in Gaza.
Lubaba Khalid, who stepped down from chairing the Young BAME (black, Asian and minority ethnic) Labour network last month, over comments made by Labour leader Keir Starmer, said she had found out on social media her relatives had been killed.
"Due to the lack of electricity and networks, we have found it very difficult keep in touch with family members just to check if they're alive," she said.
"As a result, I found out my great uncle's house was bombed, on the social-media platform X [formerly known as Twitter] before I could get any confirmation from my own family."
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Six members of her family had been killed in that bombing, she said, five of them children.
Accountant Omar Mofeed accused the UK government of "double standards" in its treatment of those evacuating Gaza.
Non-British family members of British nationals who have fled Gaza and are now in Cairo currently need to apply for British family visas from Egypt.
And Mr Mofeed pointed to the visa schemes available to those fleeing war in Ukraine, including the Ukraine Sponsorship Scheme - also known as Homes for Ukraine - and the Ukraine Family Scheme, both of which are free for those applying.
The Foreign Office has previously told BBC News it is working with the Home Office to process visas for non-British family members of British nationals who have left Gaza.