The Foreign Office said it would “continue to work tirelessly” to secure the release of more hostages after a British citizen confirmed her mother had been freed by Hamas.
Sharone Lifschitz spoke of her relief that her mother Yocheved Lifshitz was handed over by Palestinian militants, along with fellow Israeli citizen Nurit Cooper, on Monday night.
Mrs Lifshitz's London-based daughter said she would continue to campaign for the release of her father and other prisoners seized by Hamas in its bloody October 7 raids.
The Foreign, Commonwealth and Development Office (FCDO) said the department welcomed the release of two more hostages, three days after the release of an American woman and her teenage daughter.
A spokeswoman said: “Our thoughts remain with the families of our loved ones still held captive as they endure unimaginable anguish and worry at this time.
“We will continue to work tirelessly with Qatar, Israel and others to ensure that all hostages return home safely.”
Qatar is seen as a key mediator in the Middle East conflict, with Doha using its ties to Hamas – a number of figures from the political wing of the Gaza ruling group are said to be living in the country – to negotiate the release of around 220 of hostages taken during the deadly attack in Israel more than two weeks ago.
Further calls for Hamas to release its hostages are expected to be made on Tuesday during a press conference with affected families at the Israeli Embassy in London.
It comes after Mrs Lifshitz, 85, and Mrs Cooper, 79, were handed over to the Red Cross at the Rafah crossing on Monday night. They were expected to be transferred to Israel.
The two women and their husbands were taken from their homes in the Nir Oz kibbutz near the Gaza border during Hamas' rampage in southern Israeli communities.
The women's husbands have not been released.
The United States recommended that Tel Aviv delay an expected ground invasion to allow time to negotiate the release of more prisoners.
Sharone Lifschitz, in a statement, said: “I can confirm that my mother Yochi Lifschitz was one of the two hostages released to the Red Cross this evening.
“While I cannot put into words the relief that he is now safe, I will remain focused on securing the release of my father and all those, approximately 200 innocents, who remain hostages in Gaza.”
Hamas said it released the two women on humanitarian grounds.
Ms Lifschitz had spoken to the media earlier on Monday about how she had not heard from either of her parents since the Hamas ambush left 1,400 people dead and sparked fresh violence in the region, with more than 5,000 Palestinians killed in retaliation .
She described her parents as having complex health needs, telling Times Radio that her father had recorded high blood pressure the night before he was arrested.
The release comes after Prime Minister Rishi Sunak said British intelligence had concluded Israel was unlikely to be responsible for a hospital explosion believed to have killed hundreds of people in Gaza City.
Experts have been assessing the cause of the al Ahli atrocity since it happened on October 17, with Mr Sunak saying during his trip to the Middle East last week that the available evidence was still being examined.
However, in a briefing to MPs on Monday, he said the UK government had judged it “likely to have been caused by a rocket, or part of one, fired from Gaza towards Israel”.
The explosion sparked worldwide condemnation as well as competing claims about who was to blame.
Israel and Hamas both issued competing versions of events regarding the cause of the explosion, with the Palestinian group blaming an Israeli airstrike.
The Israeli military blamed a rocket from the Palestinian Islamic Jihad and released images and intercepted communications it said supported its case.
US President Joe Biden, during his visit to Tel Aviv, had sided with Israeli Prime Minister Benjamin Netanyahu and his government in assessing the tragedy.
The impact of the conflict was felt in Britain with demonstrations and vigils held in support of both Israel and the Palestinians trapped in Gaza.
Mr Sunak told MPs that chants of “jihad” by pro-Palestinian protesters at the weekend were a threat to Jewish communities and “our democratic values”.
The Prime Minister appeared to say new police powers to target voices deemed extremist were unlikely, although he pledged to “address” where there were “loopholes in the law”.
His comments came after Metropolitan Police Commissioner Sir Mark Rowley, following a meeting with Home Secretary Suella Braverman, suggested that anti-extremism legislation may need to be tightened, saying it was possible “some of the lines are not in the right place.” .