Israel continued bombing across Gaza on Wednesday evening into Thursday, particularly Khan Younis, while more cases of malnutrition are being identified due to the ongoing blockade.
At least four Palestinians were killed in Southern Gaza, while another attack in the North killed three people, Al Jazeera reported, citing journalists on the ground.
The UK's Foreign Office issued a statement saying: "Aid supplies must be allowed in, medical workers protected, and the sick and wounded allowed to temporarily leave Gaza for treatment".
The calls for evacuation come as the humanitarian situation deteriorates.
Around 3,000 aid trucks are waiting at the border, blocked from entry by Israeli forces, while Palestinians starve and organisations plead for the international community to take action.
The US on Wednesday defended Israel during the third day of hearings at the International Court of Justice, which in centering around Israel's obligations as an occupying power.
Meanwhile, wildfires that started in central Israel have triggered a "national emergency", Israeli Prime Minister Benjamin Netanyahu said on Wednesday, as the fires near Jerusalem.
Israel's fire chief said the fires are the biggest witnessed in over a decade.