Secondary school leaders are being urged do more to accommodate teachers who want to work part-time or flexibly.
A report by the National Foundation for Educational Research says there is an "unmet demand" from secondary teachers wanting to reduce or alter their hours.
It estimates that one in six teachers would like to reduce their hours - one in 12 by more than one day a week.
The government said it was supporting schools to do more to implement flexible working.
With the number of secondary school pupils in England set to increase by 15% between 2018 and 2025, the NFER's report says attracting and retaining enough teachers is "a key challenge".
The latest data for the workforce in England indicates that 19% of secondary school teachers worked part-time in 2017, compared to 27% of primary teachers.
The report says that "a lack of part-time and flexible working opportunities is an important factor contributing to some secondary teachers leaving the profession, and is preventing others from returning".