In an interview with BBC Newsnight, Mr Blunkett said the US and other developed nations should share responsibility for responding to "a global crisis".
But he said the UK needs to take "very large numbers" of refugees if it is "to be taken seriously" as a nation.
Those from Syria and women and children should have priority, Mr Blunkett said.
The former minister's intervention came as the government faced increasing pressure to commit to taking more people fleeing conflict, following the publication around the world of images of a young Syrian boy who drowned and was found on a beach in Turkey.
Mr Blunkett said: "This time we must be seen not to wash our hands and not to pretend that, good though it is, investment we are making in the camps in the region is an alternative to overcoming the sheer, blinding misery of women and children who have nowhere else to go, who are destitute".
"I understand entirely people do not want the borders opened and do not want a situation where anything goes," he added.
"How could I not understand that, having been home secretary at a time when we had to take quite drastic measures? But this is on a different scale."
Mr Blunkett was home secretary from 2001-2004, during which time he took a hard line stance and significantly reduced the number of asylum seekers accepted into the UK.
"With united agreement from the developed world and a united front from Europe, we won't have the pictures we have seen this week, we won't have the handwringing," he said.
Mr Blunkett said the photos of three-year-old Aylan Kurdi lying dead on a Turkish beach have "brought this home to people in a way that all the words that we could ever use could never do."
Speaking earlier on Thursday Prime Minister David Cameron said that "as a father" he felt "deeply moved" by the images, and said the UK would meet its "moral responsibilities" but he did not give any commitment on numbers.
Mr Blunkett's suggestion is a significant increase on the figure of 10,000 which Labour leadership contender Yvette Cooper called for on Tuesday.
The UK should take in 25,000 refugees over the next six months, former Labour Home Secretary David Blunkett has said.