Rishi Sunak said in a call with Israel’s PM Benjamin Netanyahu that the deaths of seven World Central Kitchen aid workers in the attack “appalled” him, and demanded an investigation.
WCK, which has paused its operations in Gaza, said other victims in Monday’s strike were Australian, Polish, Palestinian and a US-Canadian citizen.
Israel said the aid workers were killed by an “unintended strike”.
The team had been leaving the Deir al-Balah warehouse, where it had unloaded food aid, according to the charity.
The UK also summoned the Israeli ambassador over the deaths – the first time this has happened in 12 years.
In his call with Mr Netanyahu, Downing Street said “the prime minister said far too many aid workers and ordinary civilians have lost their lives in Gaza and the situation is increasingly intolerable”.
“The UK expects to see immediate action by Israel to end restrictions on humanitarian aid, deconflict with the UN and aid agencies, protect civilians and repair vital infrastructure like hospitals and water networks,” a spokeperson said.
“The prime minister reiterated that Israel’s rightful aim of defeating Hamas would not be achieved by allowing a humanitarian catastrophe in Gaza.”
Foreign Secretary Lord Cameron said he had spoken to Israeli Foreign Minister Israel Katz to underline the aid worker deaths were “completely unacceptable”.
“Israel must urgently explain how this happened and make major changes to ensure safety of aid workers on the ground,” he said.
“It is essential that humanitarian workers are protected and able to carry out their work.”
Meanwhile development minister Andrew Mitchell, who summoned the Israeli ambassador to the UK, said he shared the government’s “unequivocal condemnation” over the aid workers’ deaths.
Israeli prime minister Mr Netanyahu released a video message on Tuesday in which he said Israeli forces were behind the attack.
“Unfortunately, in the last 24 hours there was a tragic case of our forces unintentionally hitting innocent people in the Gaza Strip,” he said.
“It happens in war, we check it to the end, we are in contact with the governments, and we will do everything so that this thing does not happen again.”
The Israel Defense Forces (IDF) said it was conducting a “thorough review” into what it called a “tragic incident”.
But WCK chief executive Erin Gore called the strike a “targeted attack by the IDF”.
Paying tribute to the victims, Ms Gore said she was “heartbroken and appalled” at the “beautiful lives” lost in the attack.
WCK said the charity coordinated their movements with the IDF and the aid workers had been in two cars branded with WCK’s logo and another vehicle.
So far Australian Lalzawmi Frankcom, Polish national Damian Sobol and Palestinian Saif Abu Taha have been named as three of the seven aid workers killed.
Arrangements are being made to transport the bodies of the six foreigners to Egypt via the Rafah border crossing.
US-based organisation WCK aims to provide meals in humanitarian crises. The charity said it had served 42 million meals over 175 days in Gaza – working out roughly at 240,000 per day.
Last month the charity was part of the first maritime humanitarian aid shipment mission to Gaza.
An unnamed UN official told BBC News the aid worker deaths were either a “dreadful failure of deconfliction” or evidence the system that exists now is not fit for purpose.
Deconfliction is a system allowing aid organisations to work in warzones. It involves notifying military powers where aid organisations are working and when they are on the move.
Mr Mitchell also called for an “effective deconfliction mechanism immediately and urgently”.
Labour leader Sir Keir Starmer described the air strike as “outrageous and unacceptable”, as he called for humanitarian workers to be protected and international law to be upheld.
Much of the Gaza Strip has been devastated during the Israeli military operations that began after Hamas gunmen attacked southern Israel on 7 October, killing about 1,200 people and seizing 253 hostages.
About 130 of the hostages remain in captivity, at least 34 of whom are presumed dead.
More than 32,916 people have been killed in Gaza since then, the Hamas-run health ministry says.