About a third of child trust fund vouchers sent out by the government have still not been cashed and invested by parents.
Babies are entitled to vouchers for at least £250
Vouchers worth at least £250 were sent a year ago to parents to invest until their children are 18.
Two million were posted in the first wave of the scheme, but about 600,000 have yet to be cashed.
If no action is taken in the next few months, Customs and Revenue officials will choose an investment for them.
How it works
Under the scheme, children born in the UK on or after 1 September 2002 will get at least £250 each for their fund.
Families on low incomes should receive an additional £250.
The money in the CTF cannot be accessed until the child reaches 18.
However, at the age of 16, children will take over the responsibility for managing the accounts themselves.
Carl Emmerson, deputy director of the Institute of Fiscal Studies, told the BBC: "Parents may be very busy and not have time to open an account.
"The other possibility, which is much more concerning for the government, would be that parents aren't really engaged with the accounts."
"If that continues, perhaps they won't engage with the accounts over the next 17 years, which means it won't deliver the benefits that the proponents of the policy hope," he added.