But she added that this did not excuse the "many unacceptable aspects" of the Government's asylum policy, which causes trauma for many people genuinely seeking refuge in the UK.
The Refugee Council has long claimed that Britain's asylum 'problem' is actually perfectly manageable, but distorted by hostile reporting in the right-wing press and further inflamed by a Government inclined to overreact to such coverage by promising to slash refugee numbers to placate voters.
But after last week's Government's summit on immigration and asylum, Mr Blair seemed to play down the 'crisis' and pledged to get the asylum statistics verified by the National Audit Office.
Sherlock said she was relieved that at last he seemed to be trying to "lower the temperature" of the debate.
"We need a public debate on immigration and asylum that is calm and measured, and based on facts not prejudice. I hope that last week's summit saw the beginning of that process.
"The Government's focus should now be to improve the quality of asylum decisions, because getting more right the first time round creates a virtuous circle of better results, lower costs and greater public confidence."
However, she added: "There are still aspects of asylum policy that we regard as unacceptable and that should be reversed."
Not least of this is Section 55, the policy of refusing welfare support to asylum seekers who do not claim asylum immediately upon arrival. The Refugee Council surveyed 132 voluntary organisations that work with Section 55 clients, and found high numbers of them who had slept rough, and were suffering from health or mental health problems.
"Every day, we see clients in our offices who are suffering desperately at the hands of this piece of legislation," said Sherlock. "It causes nothing but harm and should be repealed."
See editorial, p17.