Research sponsored by the commission shows 86% of mothers and 83% of fathers would like some sort of flexible working arrangement and 68% of mums and 71% of dads say they do not have the working arrangement their families would prefer.
The commission argued flexible working is vital for an economy preparing for tough times ahead and it is not a business cost but an opportunity.
Nicola Brewer, chief executive of the Equality and Human Rights Commission, said: "We are disappointed to see the old-fashioned argument being made that flexibility has to be a burden instead of a potential way to increase productivity in Britain."
She added: "We need to increase the skills and confidence of managers to have the conversations with their staff that unlock genuine flexibility. Doing that would be a real investment in Britain's ability to weather the current economic and financial storms - and to raise productivity and confidence."
Equality Commission: Flexible working an opportunity not a cost
Flexible working is vital in economic downturn, according to The Equality and Human Rights Commission.
