The survey by the website KidStart found that 86 per cent of parents are against the plans to restrict the fund, which is currently available to all families.
Introduced six years ago parents get £250 to invest in the trust fund when their child is born and again on their seventh birthday. Those with a household income of less than £16,040 a year get £500 on both occasions.
But under the Conservative plan only those in the low-income bracket would receive money, a policy that KidStart estimates would leave around two-thirds of families out of pocket.
A KidStart spokeswoman said: "The majority of families in Britain earn over the £16,040 threshold. Scrapping the scheme for those households will mean a whole generation will grow up without the benefit of something that gives them such a great start in life."
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