The families say the government has left them "utterly abandoned" by not doing enough to help secure the release of their Israeli relatives.
London couple Pete and Gill Brisley's daughter, Lianne Sharabi, and their teenage grandchildren, her daughters Noiya and Yahel, were murdered by Hamas during its surprise attack on October 7.
Their son-in-law Eli and his brother Yossi were taken hostage by Hamas.
In a letter to Prime Minister Rishi Sunak the couple, both 79, described their treatment by the UK Government as "disgraceful".
In the letter, seen by The Telegraph, they reportedly wrote of their “complete and utter abandonment" by the government, and accused ministers of “impotence and inadequacy” in their dealing with the ongoing crisis.
The couple sent their letter more than a month ago, on October 24, but have reportedly still not received a specific response.
James Cleverly, who was foreign secretary when Hamas launched its attack on Israel, wrote to the couple a week after they sent their letter expressing his condolences, but officials reportedly said this was unrelated.
The couple's son Steve Brisley has told The Telegraph his family feels there has been a lack of communication and empathy from the government, as well as a lack of effort to secure the release of hostages.
"This isn’t about point-scoring," he told The Telegraph. "But my granddad landed on Juno Beach on D-Day. My parents are Londoners. My father-in-law serves in the RAF. I work in the public sector and my wife’s a classroom assistant. My nephew’s a serving officer in the Royal Navy.
“If we can’t rely on our Government in our hour of need, then, you know, is all that public service for nothing?”
He said he was disappointed neither Mr Sunak, nor recently appointed foreign secretary David Cameron, have met with his family despite having made trips to Israel.
"Rishi Sunak turns up at the King David Hotel in Jerusalem [and] bats away the BBC reporters who tried to ask him questions in the foyer, saying: ‘I need to go and meet with the families, they’re at the centre of all this'," he said. "He certainly hasn’t come and met with me.
“It just seems very much like lip service. Rishi Sunak tweeted last week about ‘we’re doing all we can’ – it’s just ‘let’s throw out a couple of tweets. Let’s do a few photo opportunities, and then let’s jump back on our plane and go back to back to the UK’.
“One thing that I found particularly difficult and contemptuous was that David Cameron visited Kibbutz Be’eri, my sister’s home, last week. So he’s trodden in the dirt into which the blood of my sister and my nieces is soaked, and yet neither he nor his predecessor has seen fit to engage with the British families.
“He doesn’t need to don a flak jacket and Kevlar helmet to engage with us."
He said his family is desperate for news of Eli and Yossi's fate. "This hanging over us is stopping us from grieving for my sister and my nieces because my whole life is consumed with this," he told The Telegraph.
Law firm Mishcon de Reya is representing the Brisleys, along with three other British families whose loved ones are being held by Hamas.
Among them is Sharone Lifschitz, a London artist and academic whose father Oded, 84, remains captive. Her mother Yocheved, 85, has been released by Hamas.
Adam Rose, a partner at Mishcon de Reya, told The Telegraph all the families are frustrated by the Government's “lack of obvious engagement”.“I don’t want to say there’s been no engagement or no activity by this Government,” he told the newspaper. “I’s just not being relayed to any of the families. It’s not being relayed to us as their advisers.
"There’s no real indication of what’s going on and, as a result, the families are just feeling hugely let down and hugely frustrated by the process.”
Mr Rose told The Standard: "We...are seeking information from the Government and a commitment for it to deliver on its promise to 'do all it can' for [the hostages].
"These hostages and their families are entitled to all of the assistance that the British state can provide, including advocacy for their release."
A Foreign Office spokesperson said it is working "around the clock" to secure the release of hostages.
“The safety of British people is our utmost priority and we are working around the clock to get them home, which is why we welcome the humanitarian pauses," a spokesperson told The Telegraph.
“The UK is involved in intensive and sensitive diplomatic efforts to secure the release of all hostages, working with Qatar, Israel, the US and others.
“Since the attacks of October 7th, we have worked tirelessly to support the British people affected. Just last week the Foreign Secretary met with the family members of hostages to directly hear their concerns, and he will continue to do so.”