The National Heart Forum, an alliance of more than 50 groups campaigning to reduce heart disease, will tell the Labour Party conference that support for the ban outweighs opposition by more than 100 to one.
Of the 1,173 non-confidential responses to the Ofcom consultation posted on its website, analysis by the Forum shows 1,109 support a 9pm restriction, including 29 national health charities and organisations, 14 consumer and public interest organisations and Ofcom's own advisory committee for England.
Jane Landon, deputy chief executive of the National Heart Forum, will tell the conference today: "These responses to their own consultation bear witness to the widespread and rising concern about the damage to children's health and well-being from commercial pressures to eat unhealthy foods.
"As Ofcom makes up its mind about what action to propose, it will surely have to rethink its notions of proportionality both in terms of the huge public health gains from a 9pm ban, and of such overwhelming public support."
The second most popular option after a watershed ban was for a fourth proposal put forward by a coalition of broadcasters and advertisers. Ofcom is against ordering a watershed on all channels, fearing it will cripple ad revenue. Broadcasters point out that the lobby's campaign includes 300 identical postcards calling for a ban, sent in by different NHS organisations.
However, some fear the issue could be seen as a vote winner and Culture Secretary Tessa Jowell has the power to order Ofcom to enforce a ban.