One in eight said they worry most about whether their offspring will ever be able to afford a home of their own. Some 4% of parents are concerned their children will expect them to contribute a deposit for a home.

Despite these concerns, the survey of 2,000 parents of kids aged up to 18 by Nationwide Savings found that 21% are not saving for their children. And of this number, 74% said that money is too tight to do so.

Of those who are saving, 47% said they put money aside occasionally, with nearly a third saving each week or month. Dads save more than mums – 32% and 27% respectively.

The average amount saved a year is £561.11, which is made up of parents’ contribution, birthday and Christmas money from family and friends, child benefit and wages from chores.

More than a third of parents (36%) save the majority of funds for their child in a tax-efficient Junior ISA or Child Trust Fund, with a further 42% choosing a different bank or building society account. The traditional piggy bank is fed by just 3% of parents and 1% now save the majority of funds for their child in a Post Office savings account or through premium bonds.

Andrew Baddeley-Chappell, Nationwide’s head of savings policy, said: “It’s clear that today’s parents are feeling under pressure to help their children achieve their aspirations in adulthood – and are well aware that all too often those dreams can only be achieved at a price. Regular saving for your child’s future can mount up over the years, particularly if you ensure those savings are tax-free. Even when you can’t afford much, establishing a savings habit with your child and a responsible attitude to money can help to safeguard their financial future.”

See YourMoney.com’s A guide to choosing a children’s savings account.