Evyatar David's family says Hamas is starving him, as the group shows a video of him being kept in a tunnel.
Negotiations between Israel and Hamas for a ceasefire and the release of hostages stalled last week.
Some say Britain's decision is an important first step – while others worry it won't make a real difference, writes BBC's International Editor Jeremy Bowen.
The visit with the IDF follows near daily reports of deadly shootings in the vicinity of the sites.
The Palestinian student, who arrived in France in July, has had her university accreditation withdrawn.
A worker has died after being attacked during a "behind-the-scenes tour" for visitors.
Layan and Mira were killed in proximity to IDF soldiers - the Israeli military says intentional harm to civilians is prohibited and their cases will be examined by the authorities.
The US says both the PLO and the Palestinian Administration continue to support "terrorism".
US special envoy Steve Witkoff will visit Gaza on Friday to inspect food distribution sites, the White House said.
Majd, 15, was almost killed by an Israeli tank shell last February. He has finally arrived in the UK for reconstructive surgery.