The march through central London led from Hyde Park to Prime Minister David Cameron's office and participants could be seen brandishing placards reading: "Open the Borders" and "Refugees In, Tories Out".
"I want to support the refugees," said Deborah Flatley, who held a homemade cardboard sign reading: "We admire your bravery. You deserve a safe and happy life. We welcome you here with open arms".
Another protester, Dusan Petkovic, told AFP: "This rally is making clear that the government is wrong in their stance towards refugees."
The premier said they would be taken directly from UN refugee camps and the British government has refused to take part in a European Union quota system to share out refugees who have already reached Europe.
Petkovic dismissed the 20,000 number as "pathetic".
Another protester, Marc Faux, said: "The government's response is ignoring the problem we have right now."
Pauline Aaron, who said she had worked in refugee camps in Africa and southeast Asia, referred to the issue of migrants in Europe as "a second humanitarian crisis" after the one in camps around Syria's borders.
A little girl held up a drawing of two hands clasped together with the words: "Help Syria, I'll be your friend".
The rally was being organised by a group of non-governmental organisations including the Stop the War movement, which was co-founded by Corbyn.
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