Prince Charles "didn't like" it when his request was refused, according to a BBC Radio 4 documentary broadcast yesterday.
Mr Blunkett, who was interviewed about the prince's involvement along with former cabinet colleagues Michael Meacher and Peter Hain, said: "Our policy was not to expand grammar schools, and he didn't like that.
"He was very keen that we should go back to a different era where youngsters had what he would have seen as the opportunity to escape from their background, whereas I wanted to change their background."
Mr Blunkett added: "I can see constitutionally that there's an argument that the heir to the throne should not get involved in controversy; the honest truth is I didn't mind. If you are waiting to be the king of the United Kingdom, and you've waited a very long time, you genuinely have to engage with something or you'd go spare."
Former environment minister Michael Meacher said he and the Prince "would consort together quietly" to affect policy on climate change and genetically-modified crops.
"I knew that he largely agreed with me and he knew that I largely agreed with him," said Mr Meacher.
"We were together in trying to persuade Tony Blair to change course."
Anti-monarchy group Republic said Charles had a "political agenda" and the Government should come clean on the extent of royal influence.