Families of captives with British links held by Hamas in Gaza said on Monday that Israel's invasion of Lebanon could distract from their loved ones being released.
Sharone Lifschitz, whose parents were taken captive during Hamas' attack on Israel last year, warned that an Israeli ground invasion of Lebanon would "take away" the focus from the remaining captives held in Gaza.
Her mother, Yocheved, was released, but her father, Oded, 84, remains in captivity.
Israel's military offensive has killed at least 41,638 people, most of them civilians, according to the health ministry in Hamas-run Gaza.
While Israel has claimed the mission was to free the hostages, Netanyahu has reportedly turned down numerous deals with Hamas that would see the captives released.
Israel has now started a brutal air and ground assault on Lebanon, launching deadly airstrikes across the country, where no Israeli captives are being held.
However, for Steve Brisley, whose brother-in-law Eli Sharabi is still being held captive in Gaza, that "takes focus away from what is the most important thing, which is the release of the captives".
He said there had been an "abject failure of international diplomacy" in securing a captive return deal and felt as though the captives had "been forgotten".
Brisley called for the UK government, which has called for a ceasefire and the release of the remaining captives, to find a "new and innovative" approach to end the crisis.
Lifschitz said there was a lack "of will from both sides", referring to Israel and Hamas.
Netanyahu has faced huge domestic criticism for not doing enough to free the hostages with the war on Gaza now widely viewed as an attempt to annex the territory for Israel and save the PM's political skin.
Meeting UK Prime Minister Keir Starmer and Foreign Secretary David Lammy earlier in the day, the family members pushed for the government to prioritise bringing their relatives back home.
"I hold the prime minister responsible for the life of these captives", said Lifschitz, adding she was feeling "encouraged" by the meeting.
Starmer told the families that "we need to see the captives returned immediately and unconditionally".
The relatives also received a message from Britain's head of state, King Charles III, and his wife, Queen Camilla, who said they "continue to keep them and all captive families in our special thoughts".