Fruity Faces, which makes novelty protective cases for fruit, invests its profits in global children's charities.
The concept cut little ice with the dragons, who refused to offer their support and branded the idea a "dangerous mix of charity and business".
The dragons – a panel of successful business people – have been accused of showing little understanding of how social enterprise works.
"We thought the dragons would want to look socially responsible, but the opposite happened," said Allen. "They said things such as: 'How can I sit on your board and take my 5 per cent when I know you're giving your 95 per cent to charity?'"
Adele Blakebrough, chief executive of support body Community Action Network, said this was a familiar response. "This is a compelling example of the hurdles facing social enterprises seeking money to grow their business," she said.
Jonathan Bland, chief executive of the Social Enterprise Coalition, said: "It's a pity the dragons have not yet realised that you can mix profitable business with achieving social dividends."
Ashish Poddar, founder of community interest company FreshTies, said the dragons had unfairly depicted social entrepreneurs as deficient.