A report said Britain had fallen short so far in its moral responsibility to help those fleeing conflict and is "turning a blind eye" to their plight.
The coalition of 13 aid agencies said Europe's overall response to the migrant crisis was inadequate and the UK should show more leadership.
The organisations include Oxfam and the Refugee Council.
They point to the fact that more than half of last year's asylum claims on the continent were made in Germany and Hungary compared with just 3% in then UK.
The groups suggest Britain could devise a new humanitarian visa that would let those at risk claim asylum remotely from their country of origin, or from a transit country, rather than risking their lives on flimsy boats.
The report also expresses concern that reception centres in hotspots such as Greece and Italy are beginning to resemble detention centres run by military personnel.
This lacks humanity and stigmatises those seeking help as if they are a security threat, it says.
British Refugee Council chief executive Maurice Wren accused European leaders of lacking the "political leadership and moral courage" to tackle the crisis.
"Today we're presenting a roadmap for change which prioritises saving lives, solidarity and safe passage," he said.
"European governments, including the UK, must take a long hard look at themselves and ask is this the best they can do? We say that it doesn't have to be this way."
According to the UN High Commissioner for Refugees, more than 135,000 migrants reached Europe by sea between January and March this year despite the creation of a European naval patrol in the Mediterranean and Aegean.
The UK needs to do more for refugees on the move in Europe, an alliance of non-governmental organisations has said.