Trust patron George Michael, along with other celebrities including singer Sade, actress Julie Walters and chef Gary Rhodes, launched the appeal in London last month.
As the trust does not receive statutory funding the new money will be extracted from the corporate sector, grant-giving trusts and other sources.
Head of fundraising Steve Brisco said the charity was planning to set up a network of local volunteer committees raising money to fund family support workers in their local community. The committees will target local businesses.
"We already have a very successful local committee in London and want to replicate this in other parts of the country," he said.
The charity will use its local contacts to persuade leading individuals in the community, including business representatives, to join the new committees. He said: "The committees will raise money in the local community and will not replace our main corporate fundraising, which is run centrally."
In addition, there will be a northern appeal and a southern appeal, as well as other initiatives such as a 'dress to impress' day, which will be promoted as an antidote to 'dress-down' days. A 'pot of gold' initiative will encourage supporters to donate unwanted or broken gold jewellery.
Brisco said the nature of the charity's work made it potentially attractive to corporate supporters: "We've been delighted with the response from the corporate sector, which I think is because we offer companies the chance to support families and children."