The money can be withdrawn when the child reaches 18
Parents of children born from the 1 September, 2002, have begun receiving letters telling them about the government's new Child Trust Fund.
The Inland Revenue is planning to send out 1.5 million letters by Christmas, advising parents about the universal savings account for their child.
In January, eligible families will receive a voucher of at least £250, or around £500 for lower-income parents.
The next step for parents will be to decide how to invest the money for their children, but government rules mean parents' choices will be limited.
As well as a cash-based account, all providers must also allow access to an alternative so-called "stakeholder" account.
This invests in shares initially but moves over to safer investments like cash and bonds when the child reaches 13.
The return on the stakeholder Child Trust Fund (CTF) might be higher than that of a cash-based account, but it is not guaranteed.
Brian Morris, Head of Savings Policy at the Building Societies Association, said many of his members prefer not to invest in shares at all and therefore will be excluded.
Speaking to BBC Radio 4's Money Box, Mr Morris said: "They feel that [investing in shares] could expose some of the customers to equity risk that [they] are not used to.
"Those customers value safe products where they know that their money could not be eroded.
"Many of our members are... locally-based organisations who have strong links with their community. It is a pity [they] are not going to be in the market for the CTF."
However, Britain's biggest building society, the Nationwide, will offer the CTF and has already begun registering interested parents.
Barclays, Norwich Union, Fidelity, Liverpool Victoria, Scottish Friendly, The Children's' Mutual, Homeowners Friendly Society, and Family Investments will also offer an account.
And Sainsbury's has just announced it will also be in the market. Its Head of Business Development Gail Quinn is hoping the big brand name will appeal to parents:
Speaking to the programme she said:
"Our relationship with consumers - particularly families in terms of their visits to the supermarket and their feelings towards Sainsbury's as a brand - left us very well-positioned to come into this market.
"There is a great opportunity for us to advertise to them while they are in shopping, buying nappies, and buying food."
An approved list of providers will be sent to parents in a government information pack in January, with the cash voucher to follow soon afterwards.
Once the account is open family or friends can contribute up to £1200 a year.
And the government has pledged to send out a second voucher when the child is seven, but the value of the second payment is not yet known.
However, a report compiled by the Personal Finance Research Group on behalf of Barclays bank, has questioned how popular topping up the funds will prove to be.
The group's Director Elaine Kempson told Money Box: "The middle class families we talked to are already saving for the children who would qualify for the CTF, and they really doubted whether they would be likely to put money into another account.
"The poorer ones however - who would be getting £500 instead of the basic £250 - were much more positive, although they doubted really whether they would be able to put money regularly into that account.
"But both groups of parents were really quite deterred by the fact that the money would be tied up until the child reached 18."
BBC Radio 4's Money Box was broadcast on Saturday, 20 November, 2004 at 1204 GMT.
The programme will be repeated on Sunday, 21 November, 2004 at 2102 GMT.