Flexible working should be the default position for all employees, rather than it being up to individuals to request.
That is the call from Conservative MP Helen Whately, who introduced a flexible working bill in Parliament on Tuesday.
It would help close the gender pay gap, assist parents to share childcare, and help businesses keep staff, she said.
Anna Whitehouse, founder of the campaign Flex Appeal, said it was "a huge moment".
Ms Whately's Ten Minute Rule Bill was given approval to go to a second reading on Wednesday.
Introducing her bill, she argued that unless employers had a sound business reason for having specific working hours, firms should introduce flexibility to every job.
"The 40-hour, five-day working week made sense in an era of single-earner households and stay-at-home mums, but it no longer reflects the reality of how many modern families want to live their lives," she said.
"At the moment, too many women are reluctantly dropping out of work or going part-time after having children because their employers won't allow them flexibility.
"This entrenches the assumption that men are the breadwinners and women are the homemakers.
"As a result, men don't get to spend as much time as they might like with their children, women miss out on career opportunities, and the country loses out on the contribution they could and would like to make - if only they could do slightly different hours or work some days from home."
Ms Whitehouse, known on social media as Mother Pukka, founded the Flex Appeal campaign after her own flexible working request was refused by her employer.
She told the BBC: "Today was a huge moment after campaigning on the streets for five years now. Now it feels like people are finally listening."
The mother-of-two, now an author and blogger, said she wanted to "open employers' eyes that there are humans driving their business", and retaining staff would be far easier if people were better able to balance their work and family lives.
Ella Smillie, from the Fawcett Society, which campaigns for gender equality, said: "We urge MPs to give Helen Whately's bill the support it deserves.
"Ensuring that employers offer flexible working would open up new jobs to a whole raft of people who want to work, alongside carrying out caring responsibilities or simply achieving a better work-life balance.
"There are also clear benefits to employers - offering flexible working to employees creates a stronger, loyal and more diverse workforce, which pays dividends."
Types of flexible working
- Working from home
- Compressed hours
- Annualised hours
- Staggered hours
- Phased retirement
Source: gov.co.uk website
Ms Whately gave an example of a male lawyer who asked his employer if he could work flexibly one day a week, only to be asked what his wife was doing.
"All these conversations start with a presumption against flexibility," the MP said. "I ask what if we flip the question and ask whether a job can't be done flexibly.
"How many more employers would find that actually it didn't make a difference where or when a piece of work was done, as long as it was done?"
MPs often use Ten Minute Rule bills to gain publicity and support for an issue they care about - they are unlikely to become law unless they get government backing.