Labour MP Catherine McKinnell, chairwoman of the Petitions Committee, made the comments in a letter to Business Minister Paul Scully.
The letter was written following a committee report last month, which recommended the Government publish new guidance around the treatment of pregnant women and new parents returning to work while there are still extremely limited childcare options available as a result of the Covid-19 pandemic.
The report was carried out after an online petition calling for statutory maternity leave to be extended by three months this year, so that new parents can have time to socialise babies with others to aid their "development", garnered more than 226,000 signatures online.
The report found that some parents had even given up their jobs as there was no "financially viable" way to extend their time off work.
In the letter on behalf of the committee, published on Tuesday, Ms McKinnell said parents are being profoundly affected by coronavirus now and "many simple cannot wait until the autumn" for action from the Government.
It read: "Parents coming to the end of their leave are faced with a dreadful dilemma of having to prepare to return to work while they try to ensure that their child's social and developmental needs are being met, at a time when finding suitable childcare is nearly impossible.
"Our investigation found some parents have even had to give up their jobs because there has been no financially viable way to extend their leave. This is having a profound impact on the mental health and wellbeing of families.
"New parents need clarity now on what support the Government will provide for them in the midst of this pandemic - this can't wait until the autumn.
"I implore the Government to act on as many of our recommendations as possible before it's too late, and have asked the Government to act immediately on several recommendations in particular that do not even require a change of policy."
The report argued that the government needs to make clear that, during the pandemic, pregnant women have the right to be suspended on full pay if they cannot work safely.
It also suggested changing the way Statutory Maternity Pay is calculated to disregard periods of unpaid leave or Statutory Sick Pay where pregnant women were put on these incorrectly.
The government said a response to the report had not been possible ahead of breaking for recess on July 22, due to the need for careful consideration of recommendations.
Ms McKinnell said: "I am extremely disappointed the Government hasn't recognised the urgency of this issue and at least responded in part to our report on the impact of Covid-19 on maternity and parental leave before the summer recess. This is particularly so given the Prime Minister's recent personal commitment to review our report."
A government spokesperson said: “The UK has one of the most generous maternity leave offers in the world, but we understand this is a difficult period for new and expectant mothers.
“We have ensured women will not lose statutory maternity pay should their roles be furloughed and we continue to offer specialist services to those experiencing mental health difficulties.
“We will respond to the Petitions Committee’s recommendations in due course.”
Additional reporting by PA Media.