The bill underwent its second reading this month and is expected to be reintroduced after the election.
Described by the EOC as 'the most radical change in sex equality law for 30 years', the bill shifts responsibility for gender equality from individuals to public authorities. It will put the burden of proof on organisations to show they have taken active steps to promote gender equality, such as through addressing unequal pay and providing flexibility in the workplace.
An EOC spokeswoman said it was 'inviting initial submissions' and would shortlist agencies for a pitch in June. EOC director of campaigns Helen Wollaston is understood to be overseeing the search.
EOC chair Julie Mellor announced this month that she was quitting after six years to become a partner at PricewaterhouseCoopers.