The broadcaster claimed the peak-time programmes, which were shown on Wednesday last week, were a measured examination of asylum in Britain.
But charities have accused the corporation of regurgitating the flawed statistics of think-tank Migration Watch and adding to public misunderstanding.
The Panorama documentary Asylum Game, which claimed to uncover the chaos at the heart of Britain's asylum system, received the bulk of criticism.
"I was revolted by the bigotry paraded on the Panorama show, which was clearly only driven by ratings," said Maurice Wren, co-ordinator at Asylum Aid. "What a wasted opportunity - the programming was trivialisation taken to the extreme."
Refugee Action is also "bitterly disappointed" over the programme. "It did little if anything to further more informed public debate, not least of all by wilfully confusing asylum with economic migration," said Leigh Daynes, communications manager at Refugee Action.
"We have already seen the negative impact of this programming on our clients, some of whom have expressed a reluctance to take part in other media projects."
The BBC's You The Judge programme, which encouraged the public to vote on whether individuals should be granted asylum, also received criticism.
"It was totally inappropriate to reduce life and death decisions to a game-show format where you had people making snap decisions without any real understanding of the issues," said a Refugee Council spokesperson.
The BBC replied: "The programmes explored this complex issue in a serious, responsible and accessible way."
Migration Watch has responded to David Blunkett's criticism of Panorama by accusing the Home Secretary of attempting to stifle debate on asylum issues. Blunkett described the Panorama programme as "poorly researched and over spun" and compared its message to that of Enoch Powell's.
Sir Andrew Green, chairman of Migration Watch, replied: "This is obviously intended to deter the BBC from any serious examination of these issues. Whatever his comments might mean, they were certainly intended as a slur and this kind of language is best avoided, particularly by a home secretary."
Although it claims not to be anti-immigration, Migration Watch's web site states the number of asylum seekers coming into Britain are "contrary to the interests of all sections of our community".
A Refugee Council spokesman said: "Many of the Migration Watch statistics simply don't stand up and it's very worrying that they were used on Panorama. This kind of programming does little to educate the public and merely reduces the debate to an even lower level."