More than one million people, including hundreds of thousands of children, are facing an "impossible decision" as a huge military assault is launched in Iraq against Islamic State (IS) fighters.
Coalition forces are backing local government and Kurdish military with air strikes in an attempt to take Mosul, the country's second largest city, back from IS rule.
Safe escape routes out of the city for civilians caught up in the bloody conflict "do not exist", Save the Children has warned.
Families and children have been advised by local forces to stay inside and erect a white flag on their homes in a bid to stay safe, the charity's spokesman, Ruairidh Villar, said.
Speaking from Irbil, he told the Press Association: "Whether families and children stay or they flee, right now it's an impossible decision."
Save the Children, which said humanitarian agencies are able to get no closer than 30 miles (48km) to the city, is calling on people to urge the Government to do what it can to ensure there are safe pathways for people to leave the area.
He said: "We are calling on the UK Government to put pressure on the Iraqi and coalition forces around Mosul now to establish safe corridors, safe escape routes for children to get out."
Children in Mosul, which has been under IS control for two years, face further trauma amid the bombardment of the city, Mr Villar said.
"These children have been through two years of IS rule, subject to an education which is focused on extremist violence," he said, adding that much planning has gone into military operations but not necessarily the humanitarian fallout.
"Some children have not gone to school at all. There's been a lack of food and medicine and after all that they're going to have to escape from what looks to be a very bloody conflict indeed."
The charity said the UN's emergency appeal is not well enough funded, meaning camps only ready to house around 60,000 people could be "overwhelmed within days".
Save the Children is providing emergency water supplies, dried food, soap and other items to newly displaced families, and has appealed to people to donate to their campaign to help those affected.