She was expected to move in the 1999 reshuffle, but Education Secretary David Blunkett is said to have told Tony Blair he did not want his trusted sidekick to leave.
Ms Morris comes from impeccable Labour party stock: her father, Charles, and uncle, Lord Morris of Manchester, were both MPs.
She began her political career as a councillor in the Midlands and was elected MP for Yardley, Birmingham in 1992 with a slender 162 majority, increased to 5,315 in 1997.
Almost a year before the last election she set out Labour's intentions in The TES, saying the party was anxious to raise morale in the profession after 17 years of curriculum changes, poor funding and pay.
But the schools standards minister added: "We don't pretend that soothing words will make everything all right. The challenge is bigger than that."
She hit the ground running. After 100 days in office as a junior minister, she had already opened specialist schools, announced education action zones, given details of new indicators for league tables, and called fo a sharper focus on numeracy and literacy.
With her then boss, Stephen Byers, she met representatives from all 18 schools "named and shamed" by him.
By the following summer she had taken Mr Byers' place on his move to trade and industry. It was said she had done much of his work as well as her own.
She is single and doesn't list any hobbies in the reference books. According to Andrew Roth's gossipy Parliamentary Profiles, she is "deceptively frail and quiet voiced"; has a "will of steel": is "tougher than she looks; you don't mess with Estelle". If all this is true, Ms Morris could be a fitting successor.
Born 1952, Manchester
Educated Whalley Range high school, Manchester; Coventry College of Education (TCert); BEd Warwick University
1974-1992:PE and sports teacher then head of sixth-form studies at Sidney Stringer school and community college, Coventry
1979-91: councillor, Warwick District Council
1982-89: leader of Labour group
1992: MP for Birmingham, Yardley
1994-5: Opposition whip
1995-7 : Opposition spokeswoman on education and employment
1997-8: parliamentary under-secretary, Department for Education and Employment, school standards
1998-: Schools standards minister