Some 1,500 migrants live in very poor conditions outside Calais
The Refugee Council has said granting asylum to a small number of vulnerable migrants from Calais' illegal camp might be the "right solution".
It wants the UK to grant entry to some migrants, particularly children, with family connections in the UK.
The UK Border Agency has rejected calls for Britain to accept refugees from the camp known as "the jungle".
Last week French officials announced the camp, home to about 1,500 migrants, would soon be be shut down.
Donna Covey, chief executive of the Refugee Council, told the BBC's Today programme: "There are a small number of very vulnerable people, particularly children, in the 'jungle', for whom - because of family connections - asylum in the UK might be the right solution, both under our rules and international rules."
You have to look at the system as a whole, you can't just say there are vulnerable children
Sir Andrew Green
Migration Watch UK
But Sir Andrew Green, of Migration Watch UK, said Britain was already seen by many would-be migrants as an easy country and enter and remain.
He said: "We entirely support asylum for genuine cases, but it seems Britain is now seen as a soft touch.
"That's certainly what the French believe - why else should people be queuing up in Calais when France is a safe country?"
Over the last nine years, people arriving in the UK who said the word "asylum" had had an 80% chance of staying, he said.
"The system is not working, we're not removing people who have no right to be here, the system's costing us about £2 million a day.
"You have to look at the system as a whole, you can't just say there are vulnerable children," he said.
But Ms Covey denied Britain was a soft touch.
She said asylum seekers normally had "very little information about the British system", but came to the UK because of historic links, family, or because "it's where they end up being smuggled to".
Both France and Italy had received more claims than Britain in 2008, and less than one third of asylum seekers who claimed asylum in the UK "received any protection in the end", she said.
Calais' "jungle" has replaced official refugee centres like the now-closed Sangatte as a gathering point for migrants hoping to cross to Britain.
Most are from Iraq and Afghanistan, and are now living in insanitary settlements close to the port.
France's Immigration Minister Eric Besson told French television that imminent closure of the "jungle" would send a strong message that people traffickers could no longer use Calais.
The UN's High Commissioner for Refugees, Antonio Guterres, has asked the British government to consider granting entry to migrants who already had large families in the UK.
But the UK Border Agency said genuine asylum seekers should make their claim in the first European country they enter.
Mr Guterres also called on all European countries to work more effectively together to standardise their asylum policies.