Despite the significant challenges of getting aid to people who most need it in southern Somalia, one of the world's most dangerous places, Mr Mitchell will report that over 800,000 people there are being reached with food assistance.
As concerns rise about the likely impact of disease on people in Somalia made weak and vulnerable by months of hunger, Britain is also supporting the vaccination of 1.3 million children against measles and 670,000 against polio.
In addition, Britain's humanitarian assistance to the Horn of Africa has already delivered emergency food for 2.4 million people in Ethiopia and safe drinking water for 300,000 Somalis in Dadaab refugee camp, northern Kenya.
Speaking in advance of the UN General Assembly, Mr Mitchell said:
"October threatens to be the critical month in Somalia. In a bitter irony, the rains that are so desperately needed – and will help recovery in the long term - will bring disease that threatens the lives of hundreds of thousands of vulnerable people, weakened by hunger.
"Getting aid into conflict-ridden Somalia, the epicentre of this crisis, is incredibly hard. But with so many lives at stake, this is no time for excuses. British assistance is saving lives, and I pay tribute to the brave, committed humanitarians who are risking their own safety to help others.
"The international community must now dig deeper into their pockets to ensure that emergency aid gets to those people who will continue to need it until the end of the year and beyond. Britain has taken a lead role, others should not be happy as merely bit part players."