Refugees heading to Europe will be urged to settle in Asia and Latin America instead, under a new €35m British aid package.
Meanwhile, the German government has budgeted more than €40 million to pay asylum seekers to voluntarily return to their home countries.
Theresa May announced the scheme at an EU summit in Malta, arguing it showed the government is “stepping up its support for the most vulnerable refugees”.
The package will see Britain provide lifesaving supplies for people facing freezing conditions across Eastern Europe and Greece, including warm clothing, shelter and medical care.
However, it will also pay for better infrastructure in far-flung countries willing to take refugees who had hoped to settle in Europe.
The move builds on an existing scheme run by The UN Refugee Agency (UNHCR), but it is the first time Britain’s aid budget has been used to bolster it.
Only a few thousand Syrian refugees have been resettled in Britain – and the government has refused to take part in an EU-wide programme to co-ordinate the continent’s response to the crisis.
Government sources stressed that people would only be diverted to countries in Asia and Latin America if they were willing to be resettled there.
The Department for International Development is expected to release a list of interested countries later.
In Germany, migrants will be offered financial incentives of up to €1,200 each to leave the country and withdraw their application for protection, with a lower amount of €800 if they choose to depart after being refused asylum.
Germany is the latest European country to boost “voluntary return” programmes amid growing anti-immigration sentiment across the continent.
Denmark’s initiative, also run with the IOM, caused 532 asylum seekers to voluntarily leave the country last year – a record number.