The shadow home secretary told the BBC’s Political Thinking podcast that, in her early days in politics, women MPs had been reluctant to be seen “juggling” work and family duties.
As a result, she had feared not looking “professional” in front of the then PM, who was boarding a train she was on.
Ms Cooper had three children after entering Parliament in 1997, aged 28.
At the general election that year, won by Labour, the number of women MPs doubled to 120 – by 2019 the figure had risen to 220.