Yahel, 13, was killed along with her mother, Lianne, while her elder sister, Noiya, 16, and her father, Eli, are still missing, the BBC reported.
The teenager, whose family name has not been revealed, disappeared after militants attacked Kibbutz Be’eri and killed her British-born mother.
The 13-year-old’s death was confirmed by her family, the BBC said.
The development came as Foreign Office minister Andrew Mitchell said the Government is “extremely concerned” about British hostages being held by Hamas following the October 7 attacks and “we pray that they are alive”.
Up to 10 hostages are feared to have been taken and Mr Mitchell promised the UK is doing “everything” possible to rescue them.
On Monday, Prime Minister Rishi Sunak told MPs that at least six British citizens were killed, with a further 10 missing, some of whom were feared to be among the dead.
Mr Mitchell told BBC Breakfast: “We mourn the six British hostages we know who have died and we are extremely concerned about the fate and the state of the other 10.”
He told Sky News: “We pray that they are alive.”
Mr Mitchell was unable to elaborate on the efforts to secure their release, but insisted to LBC: “The entire resources of the British Government are involved in doing everything we can to get our citizens back.”
At least 1,400 people were killed, many of them civilians, and thousands more injured in Hamas’s attack.
More than 2,700 Palestinians have died as Israel launched air strikes on Gaza and cut off fuel, water, food and medical supplies from entering the cramped territory, which is home to more than two million people.
British officials are working to secure the opening of the Rafah crossing to allow Britons to flee to Egypt and for humanitarian aid to get into Gaza.
On Israel’s role, Mr Mitchell told Times Radio: “It’s both a moral and a practical responsibility. We stand absolutely foursquare behind Israel’s right to defend itself, but all of us want to see the fighting contained.”
Mr Mitchell told BBC Radio 4’s Today programme that US President Joe Biden’s visit to Israel could be a “significant fillip” to getting humanitarian relief through.
Mr Biden was travelling to Israel and Jordan on Wednesday amid concerns the Israel-Hamas war could spiral into a wider regional conflict.
As well as his talks in Israel, the US president will meet King Abdullah of Jordan, Egyptian President Abdel Fattah El-Sisi and Palestinian President Mahmoud Abbas.
Israeli air strikes continued early on Tuesday, even inside the evacuation zone where Israel had told residents to gather in advance of the expected ground assault on Gaza.