Currently, workers have limited protection against being dismissed when they are on maternity leave.
Under the new law, this protection will begin from the moment a woman tells her boss she is pregnant until the child is 18 months old.
The Pregnant Then Screwed charity said Labour MP Dan Jarvis's bill was a "step in the right direction" but needs more legal backbone.
Mr Jarvis's bill, was approved by MPs on Friday and will now be debated in the House of Lords.
However, as it has government support it is likely to become law and will apply to England, Wales and Scotland, but not Northern Ireland where employment law is devolved.
The Barnsley Central MP - the former mayor of South Yorkshire - said it would help the "tens of thousand of women pushed out of the workforce every year simply for being pregnant".
Currently, the Maple (Maternity and Parental Leave Regulations 1999) say that an employer should not make a woman on maternity leave or a parent on shared parental or adoption leave redundant and they are obliged to offered them a suitable alternative vacancy where one exists, if their job is at risk.
Mr Jarvis's bill would extend the right to pregnant women as well as new parents returning to work.
Women already have some protection under the Equality Act which states that an employer cannot discriminate against someone because they are pregnant or on maternity leave. There are also employment laws which protect people from being dismissed from their job unfairly.
However, Pregnant Then Screwed director Joeli Brearley said very few women are able to challenge employers who ignore the current protections because the legal system isn't on their side.
And, she added, women are often not made redundant but simply put in a position where they can no longer keep working.
This is because their employer refuses to grant them part-time or flexible working arrangements.
Sarah faced that problem when, in 2021, she told her employers she was pregnant.
She says her relationship with her bosses deteriorated when, five months into her pregnancy, her request not to be put on shifts where she would be on her feet for more than six hours was refused.
And after her baby was born, she says her employers rejected a request for part-time or flexible working and instead simply offered her a demotion and a pay cut.
"I don't want any other woman to go through what I went through. It broke my heart," she said.
Sarah felt she had no option but to leave the job. She is hoping a tribunal will still consider her case against her former employer, who the BBC understands disputes her claims.
Pregnant Then Screwed is campaigning for the government to extend the current three-month limit on bringing unfair dismissal claims to six months, which it says will encourage more women to challenge discrimination.
Joeli Brearley argues that the time and expense puts women off pursuing a case.
"Some women are waiting more than two years for their first hearing - nobody wants that hanging over their head.
"It is also very expensive. If you hire a lawyer cases can cost up to £40,000 to 50,000."
She added that trying to learn employment law when you are a pregnant or a new mother was "just not possible".