It comes as Commons Speaker, Chorley MP Sir Lindsay Hoyle, requested a review into whether MPs can take babies into the chamber amid an outcry.
Blackpool South's Tory MP Scott Benton went against seemingly popular opinion, however, tweeting: "Parents who get paid a fraction of what you do pay for childcare and juggle responsibilities so they can go to work. What makes you so special?”
He later added: "If you phoned 999 you wouldn't expect the police to turn up with their children in tow so why would you tune into Parliament TV and expect to see MPs with their children?"
Ms Creasy received the warning in an email from the private secretary to Deputy Speaker Dame Eleanor Laing and was referred to the section of the MPs’ rulebook, which was updated in September, stating they “should not take your seat in the chamber when accompanied by your child”.
Speaking to The Gazette during a visit to Blackpool yesterday, Ms Rayner, Labour's deputy leader, said: "I think mums should be able to work flexibiy.
"My colleague is highlighting a very serious issue that, actually, members of parliament do not get maternity leave.
"If Stella doesn't come in to represent her constituency, nobody represents her constituents, so she's trying to make a broader point here -- about making sure that everybody, regardless of what your job is, whether you are an MP, whether you are working in the retail industry or any other industry in the country, you should be able to get some level of flexibility on working rights."
Mr Hoyle stressed it is “extremely important” that parents can fully participate in parliamentary work as he asked the Procedure Committee on Wednesday to bring forward recommendations for the House to make a ruling.
Ms Creasy, a mother-of-two, welcomed the review after she was contacted by authorities after bringing son Pip into a Westminster Hall debate on Tuesday.
Tory former minister Paul Maynard, MP for Blackpool North and Cleveleys, had told the debate: “I congratulate Pip on taking the sensible decision to fall asleep during his mother’s speech.
“He had a nice long sleep, as we can all observe, which was perhaps a sensible decision by him.”
Sir Lindsay said he was unaware that the warning was going to be issued to Ms Creasy but accepted it “correctly reflects the current rules”.
“However, rules have to be seen in context and they change with the times,” he told MPs in a statement when he opened the Commons on Wednesday morning.
“This House has to be able to function professionally and without disturbance. However, sometimes there may be occasions when the chair can exercise discretion assuming to the business not being disturbed.
“I accept there are differing views on this matter.”
He said Procedure Committee chairwoman Karen Bradley would review the matter and bring forward recommendations which will be “ultimately for the House to take a view on”.
Ms Creasy said she hopes the move “means some of these rules will be reviewed to make parenting and politics possible to mix”.
Pip, who is breastfeeding, has regularly attended the Commons, as did Ms Creasy’s older daughter.
Labour MP Alex Davies-Jones had written to Sir Lindsay calling for “urgent clarification” on the rules, after saying the warning left her and other mothers “hugely concerned”.
Ms Davies-Jones said the warning appeared to be a “contradiction” to Sir Lindsay’s assurance in January last year that he “wouldn’t be upset by” a mother deciding to breastfeed her baby in the chamber.
Caroline Lucas, the Green MP, said the rule is “absurd” and “absolutely needs to be challenged”, adding that babies are “far less disruptive than many braying backbenchers”.
Deputy Prime Minister Dominic Raab said he has “a lot of sympathy” for Ms Creasy and said he would not be distracted at the despatch box by the presence of a baby.
“I think we do need to make sure our profession is brought into the modern world, the 21st century, and can allow parents to juggle the jobs they do with the family time that they need,” he told BBC Breakfast.
“When you see your colleagues with their children given the rough and tumble of politics, I just always think it brings out the best in people.
“Whether it’s the right thing in the chamber, there will be different views on that, it will be for the House authorities to decide, but it certainly wouldn’t distract me or get in the way of me doing my job.”
A House of Commons spokesman said authorities are “currently in communication” with Ms Creasy about the issue.
In late September, Ms Creasy’s then-newborn was strapped to her as she rose in the chamber to ask Jacob Rees-Mogg to ensure new mothers were supported rather than “rebuked” when returning to Parliament.
The Commons Leader responded that the rules were “perfectly reasonable and entirely in line with the law”.
Former Liberal Democrat leader Jo Swinson was believed to be the first MP to take her baby into the chamber during a debate, when she cradled her son on the Commons’ green benches in September 2018.
Meanwhile, Leicester West MP Liz Kendall said she will be stepping back from her parliamentary duties and her frontbench role temporarily next year when she has a new baby through surrogacy.
It is thanks to our loyal readers that we can continue to provide the trusted news, analysis and insight that matters to you. For unlimited access to our unrivalled local reporting, you can take out a subscription here and help support the work of our dedicated team of reporters.