The report also called for qualified teachers in nurseries to ensure children are properly stimulated.
It found over 130,000 children are already falling behind in language skills before they reach school.
"Toddlers' brains are like sponges, absorbing knowledge and making new connections faster than at any other time in life," said Save the Children's director of UK poverty, Gareth Jenkins.
"To tackle the nation's education gap, we need a new national focus on early learning to give children the best start - not just increasing free childcare hours, but boosting nursery quality to help support children and parents with early learning."
The report included a survey of 1,000 parents finding that almost half had low expectation for their child's early learning. Also 56% of parents felt they needed more advice to understand their child's early learning.
Christian childcare expert, Rachel Waddilove, says qualified teachers would be a welcome addition but thinks parents are capable of meeting the learning requirements. She says they simply need to engage with their children.
Speaking on Premier's News Hour, she said: "Parents should play read, sing, with their children, take them out for walks and show them things.
"I think the danger we are seeing today is lots of young children are sat in front of a screen."
The report called Lighting Up Young Brains, was written in conjunction with University of London's Institute of Child Health. A neuroscience professor at UCL said: "It is precisely this period where we have explosive brain growth, where most of the connections in the brain are formed.
"And we know that if these connections are not formed they, to variable degrees, will suffer longer-term consequences to their physical, cognitive but also emotional development."
Childcare Minister Same Gyimah has said the government is committed to developing early childhood care and education, including raising salaries and the status of professional workers.