The UK will provide another £20m of aid for Syria, as the Prime Minister condemned Bashar al Assad and his Russian and Iranian backers.
Theresa May said the Syrian government must let the United Nations ensure the safe evacuation of civilians from Aleppo.
President Assad has claimed victory in the city, which had been held by rebel fighters for more than four years.
Speaking as she left the European Council summit in Brussels, Mrs May said the UK would provide extra funding for the most vulnerable people in Syria.
The PM said: “We have discussed a number of issues here today at this European Council meeting, including how to deal with migration issues, also strengthening Europe’s security.
“But perhaps the most important issue we discussed was the appalling situation in Syria.
“We heard from the mayor of eastern Aleppo, he had one plea for us: to allow the safe evacuation of the people in the city.
“President Assad and his backers, Russia and Iran, bear responsibility for the tragedy in Aleppo. They must now allow the United Nations to ensure the safe evacuation of the civilians who are left there.
“The UK is going to provide a further £20m of practical support for those who are most vulnerable.
“The mayor of east Aleppo said to us that we can’t bring back those who are lost but we can save those who remain and that is what we must now do.”
International Development Secretary Priti Patel said the UK was urgently sending blankets, medical kits, clean water and food for civilians from Aleppo.
She said the aid would “mean the difference between life and death for those fleeing Aleppo and those caught in freezing conditions in the city after being systematically bombed from their homes by the Syrian regime and its Russian allies”.
Ms Patel added: “Protecting innocent civilians must be an absolute priority.
“It is paramount that aid agencies now get the unfettered, secure access they need to save lives inside east Aleppo.”
US Secretary of State John Kerry has accused President Assad’s regime of carrying out “nothing short of a massacre” in Aleppo.
It comes as thousands of civilians started to leave the east of the city, headed for rebel-held areas outside Aleppo as part of a ceasefire deal.