A survey of 2,000 adults and 500 businesses, also found that one in five of those without children believed parents receive better support with flexible work arrangements.
The study, by Scottish Widows' think-tank the Centre for the Modern Family, showed a third of employers worried that they could not afford to go beyond what is legally required on flexible working.
Most medium-sized firms would never consider offering full-time working from home, said the report.
Anita Frew, who chairs the Centre for the Modern Family, said: "Although employers have taken promising steps towards offering more flexible working hours, there is still work to be done to ensure these policies are being rolled out to all employees.
"Our economy depends on a skilled and motivated workforce that functions productively, and our best hope of achieving this is through encouraging employers to adapt to the evolving needs of the workforce.
"Targeted support is essential to help employers understand the benefits for their business, but practical support is crucial in order to navigate the complex challenges around the implementation of more flexible initiatives and practices."