It brings the total UK assistance to Iraq since June 2014 to £79.5m.
The money will pay for food, medicine, shelter and clothing, and provide clean water and improved sanitation to help prevent the spread of cholera.
Minister Desmond Swayne said "the world's gaze appears to have wandered" from the suffering of those in Iraq.
The so-called Islamic State controls swathes of Iraq's territory, and in places where it has implemented its strict interpretation of Sharia, women are forced to wear full veils, public beheadings are common and non-Muslims are forced to choose between paying a special tax, converting or death.
More than eight million people require humanitarian assistance inside Iraq, with 3.2 million Iraqis internally displaced.
Speaking during a visit to the country, Mr Swayne said: "We cannot separate out what is happening in Iraq from the instability gripping Syria and the wider region.
"The UN's latest appeal is seriously underfunded and we do not want to see more Iraqis being forced to move because they cannot get the help they need where they are.
"Donors must step up to meet the shortfall now, to prevent Iraq's problems spilling over its borders."
In June, the UN warned that critical aid operations supporting millions of people in Iraq were at risk of shutting down without an urgent increase in funding.
It is appealing for nearly $500m (£330m) to cover the immediate needs of 5.6 million Iraqis for the next six months.
The UK is giving another £20m in aid to help tens of thousands of Iraqis forced to flee their homes by the Islamic State terror group.