Around one in three parents do not know if their child is being taught by a qualified early years teacher, according to a poll.
The majority of mothers and fathers would rather their youngster was taught by someone who specialises in early years education, while many think that ministers should ensure there is a qualified teacher in every nursery.
The Save the Children poll reveals that while half (51%) know that their son or daughter's nursery has a teacher who is trained to degree level, some 34% said that they do not know if that is the case.
Around half (51%) agreed that they would be worried about sending their child to an establishment with no qualified early years teacher, and around seven in 10 (71%) said they would rather send their pre-schooler to a nursery with a qualified teacher than a nursery that does not have one.
Around three quarters (74%) said that the Government should ensure that every nursery has a qualified member of staff.
Save the Children said it had calculated that by 2020, around 800,000 young children will be at risk of not reaching a good level of development at age five, and that of those who start school behind, around a quarter are likely to remain behind in English by the time they reach secondary school, with around a fifth behind in maths.
Well-qualified nursery staff can help ensure youngsters get a good start to their education, the charity suggested.
Chief executive Kevin Watkins said: "It's just not acceptable that in this day and age, so many children in England are falling behind before they even set foot in primary school - leaving them at risk of staying behind throughout their school years and into the world of work.
"Nurseries do an incredible job nurturing our children, but financial constraints are leaving many of them struggling to hire the qualified early years teachers who help give children the skills and confidence they need to learn and grow.
"The evidence clearly shows the huge and transformational difference early years teachers can make for children.
"That's why we're calling on the Government to ensure every nursery has a qualified teacher. It's an investment we must make to help every child reach their full potential."
The findings come just days after researchers suggested that children who have access to a qualified teacher at nursery do only slightly better at age five than their classmates.
A new study concluded that a youngster's educational achievement at the end of their reception year is only very slightly higher if they have been taught in a nursery with a teacher trained to graduate level.
The YouGov poll questioned 3,070 parents with children aged 18 and under, including around 944 youngsters aged five and under.
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