She announced her decision with a sideswipe at the culture of spin and the Government's failure to connect with voters.
Ms Morris said: "If I have a regret it's that our government - and not just Labour, it's not about parties, it's about all of us, Labour and Tories - has failed to find a language that the public understands.
"The two major parties have coalesced around a series of statements that they think define themselves with the public. And they don't. There's too much about soundbites and headlines."
Aside from the unusual manner in which she quit the Cabinet, Ms Morris will be remembered for introducing a more conciliatory approach towards the teaching unions and for beginning negotiations to cut teacher workload, talks that eventually led to the workforce agreement.
She has been the Labour MP for Birmingham Yardley since 1992 and was an education junior minister for four years before taking over the department in 2001, when David Blunkett moved to the Home Office.
Ms Morris, a former teacher, remains well regarded by a profession she sought to modernise by persuasion rather than dictat.
She decided to quit as education secretary after a row over A-level marking and Labour failed to hit its primary literacy and numeracy targets.
Ms Morris said in her resignation letter that she was not up to the strategic management of a large department, but she is believed to have felt she had little option but to go after promising MPs she would resign if schools failed to hit the targets.
She later returned to the Government as an arts minister. Ms Morris said:
"I am tremendously proud of the achievements of the Labour Government and the contribution I have been able to make in two departments of State.
"I have not lost my enthusiasm or energy for politics but I want a different focus and a new challenge outside the House of Commons."
Steve Sinnott, general secretary of the National Union of Teachers, paid tribute to Ms Morris, a member of the NUT.
"We are sorry to hear that Estelle is to leave Parliament," he said. "We were disappointed when she gave up as education secretary. She was a loss to the service. She will be sadly missed from politics."