Foreign Secretary Lord Cameron has said Israel needs "a whole series of warnings" over the amount of aid reaching Gaza.
The foreign secretary said he would be starting with Benny Gantz, a retired general and member of the Israel's war cabinet who he is due to meet later.
Lord Cameron told peers that "patience needs to run very thin" with Israel.
And he said there was "dreadful suffering" in Gaza, with people dying of hunger and preventable disease.
Speaking during a debate on foreign affairs in the House of Lords on Tuesday, he said that despite the UK pushing for more aid to get into Gaza, the amount that had reached the territory in February was just half that of the previous month.
As the "occupying power", Lord Cameron said Israel was "responsible" and that this had consequences under international humanitarian law.
International law states that an occupying power has a duty to ensure food and medical supplies to the population under its control "to the fullest extent of the means available to it".
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"I spoke some weeks ago about the danger of [the situation in Gaza] tipping into famine and the danger of illness tipping into disease and we are now at that point," Lord Cameron said.
He added: "So patience needs to run very thin and a whole series of warnings need to be given starting I hope with a meeting I have with Minister Gantz when he visits the UK."
Mr Gantz, who is travelling against the wishes of Prime Minister Benjamin Netanyahu, is visiting London after his trip to Washington.
The moderate chairman of Israel's National Unity Party, Mr Gantz has proved a stiff political opponent to Mr Netanyahu, despite joining him as a member of his war cabinet after the attack nearly five months ago by Hamas that triggered the conflict.
While he was in the United States, Vice-President Kamala Harris expressed "deep concern" over the situation in Gaza and urged Israel to allow more aid in, while calling on Hamas to accept terms for a ceasefire.
On 7 October, Hamas gunmen stormed across Gaza's border into Israel, killing about 1,200 people and taking more than 250 others as hostages.
In response, Israel launched a campaign of air strikes and a ground invasion of the territory.
More than 30,000 Palestinians have been killed, and tens of thousands injured by Israeli strikes since the start of the war, according to Gaza's Hamas-run health ministry.
