Dr Maisara Al Rayyes, 30, was photographed with Foreign Secretary James Cleverly after meeting him alongside other graduates of the programme two months ago.
He was trapped under the rubble of a six-storey apartment building which was razed to the ground in Gaza City on Sunday night.
The UK's handling of the case has triggered anger among some Foreign Office staff, the BBC understands, amid wider complaints over a failure to explicitly highlight the spiralling civilian death toll in Gaza.
It has also sparked a fierce backlash from some of the medic's former colleagues and scholarship members.
Dr Al Rayyes was a graduate of the Chevening Scholarship scheme, an elite programme run by the Foreign, Commonwealth and Development Office (FCDO).
The scheme is seen as a pillar of British diplomatic prowess, funding places at UK universities for overseas applicants it describes as global "leaders and decision-makers" of the future.  More than 15 Chevening graduates have gone on to become heads of state.
The story of Dr Al Rayyes, who won funding for a master's degree in health at King's College London, was embraced by the Foreign Office especially as he met his fiancÃ©e, another Chevening scholar, via the programme.
In September he was chosen among a select group of graduates to meet the Foreign Secretary in Jerusalem.
On Monday, Dr Al Rayyes's parents and a nephew were found dead in the rubble of the family home, friends say, while Dr Al Rayyes himself is yet to be recovered.
It has not been possible for BBC journalists to visit the scene to verify what happened on the ground. Videos of the aftermath show the apartment block completely collapsed, with the concrete structure of each floor compressed into the next, forming a vast area of compacted wreckage and tangled metal.
The Israeli military declined to respond to questions about the incident.
On Wednesday morning, the BBC attempted to make contact with Dr Al Rayyes's younger brother Moayed who was said to have witnessed the strike from a neighbouring house. He was spending a third day along with another sibling searching for Dr Al Rayyes in the rubble.
But on Wednesday afternoon while still trying to reach their brother, Moayed and his older sibling Mohammed Al Rayyes were killed in another blast on the street, family friends say.
Video showed their bodies on top of the wreckage. A local journalist documenting the rescue scene was also wounded.
The Foreign Office on Wednesday said it was "devastated" andoffered condolences to the surviving familyand "Chevening Alumni community" over the death of Dr Al Rayyes but didn't give any details about what happened to him, or where.
The post triggered a storm of criticism from users on X, previously known as Twitter, including from some of his former medical colleagues who accused the UK of trying to avoid any criticism of Israel.
The handling of his case also sparked "huge amounts of discontent" among some UK officials who felt the death announcement was not placed in context, according to accounts of events described to the BBC.
It is also understood "staff counsellors" in the Foreign Office have been collating internal concerns raised about the government's position on the Israel-Hamas war, and briefing senior officials on their contents.
These have included claims the government has shown a permissive approach to Israel "breaching international humanitarian law" given the unprecedented scale of the civilian death toll in Gaza, and that this could damage wider foreign policy, for example, when it comes to highlighting breaches of the global rules-based order by Russia in Ukraine.
On Monday, a group representing Chevening graduates in 28 countries wrote to the foreign secretary pleading with him to protect their colleagues and "focus on the needs and safety of Chevening Alumni" in Gaza and "work towards an immediate ceasefire".
One Chevening graduate has since accused the Foreign Office of whitewashing Dr Al Rayyes's death.
Hala Hanini, a Chevening graduate and close friend of Dr Al Rayyes, told the BBC it was "disgusting, disappointing and outrageous" that the government tweeted its sympathies but did not raise any questions over how he was killed.
"It's as if he just died of normal things," she said. "[UK ministers] claim that Israel has the right to self defence butâ¦ it actually has responsibilities over the occupied people to provide them with safety, securityâ¦ [instead] they are committing genocide and calling it in a false way self-defence," she said, accusing the UK of failing to uphold international law.
Asked about the concerns raised, the FCDO declined to comment, telling the BBC "we wouldn't have anything to add beyond the tweet" about Dr Al Rayyes.
In Gaza more than 10,500 Palestinians have been killed in just over a month according to the health ministry in the territory, which is governed by Hamas and has been blockaded by Israel and Egypt since 2007.
The UK government has previously given its "unequivocal" support to Israel saying it has a "right to defend itself" following the 7 October attacks by Hamas which saw 1,400 people killed and more than 240 taken hostage.
The UK has also called on Israel to observe international humanitarian law in its response.
Israel says its strikes have targeted "Hamas terrorists and infrastructure", blaming the group for deaths of civilians by using them as "human shields".
Many Palestinians accuse the Israeli military of deliberately targeting civilians in order to add to the pressure on Hamas. Israel has said it will not agree to any pause in the fighting until hostages are released.
A Palestinian doctor who graduated from a prestigious UK Foreign Office scholarship scheme is feared to have been killed along with most of his family in an Israeli air strike in Gaza, colleagues say.