Coca-Cola warned the education secretary it might withdraw its vending machines network from schools over her ban on "junk food", letters show.
Coca-Cola wanted low sugar drinks to be "highlighted as acceptable"
The company told her last November that the proposed ending of fizzy drinks sales would make the business unviable.
It said schools would lose money and pupils would suffer from the removal of such "a highly efficient country-wide beverage distribution system".
The minister, Ruth Kelly, declined Coca-Cola's request for a meeting.
She noted that the company was represented in an industry delegation that met one of her officials.
The exchange of letters was obtained by the BBC's Freedom of Information Unit.
The background was the proposed ban, announced by Ms Kelly at the Labour conference.
This week, the School Food Trust, set up to advise on children's eating habits, recommended that the only drinks available should be fresh or bottled water, skimmed or semi-skimmed milk, pure fruit juices, yoghurt and milk drinks or combination drinks such as smoothies, low calorie hot chocolate, tea and coffee.
Coca-Cola's letter argued that many soft drinks provided "significant nutritional and functional benefits".
As an example, one "no added sugar" product - which contains two artificial sweeteners - was fortified with vitamins and minerals.
The fruit and water mixture, it said, provided one of the recommended "five a day" servings of fruit and vegetables.
The company queried the assumption that if pupils were offered a restricted choice they would purchase something healthy rather than nothing at all.
The risk, it said, was that they might instead put off having a drink "until a more popular choice was available" - with a significant impact on their hydration, concentration and performance.
The letter said its commercial experience suggested that in the longer term its existing business model would not be viable or profitable.
"We would, in addition, almost certainly be unable to deliver the significant revenue gain that many schools currently enjoy from vending."
Withdrawing its machines - which were in schools at their request - was "a real possibility".
"The removal of such a highly efficient country-wide beverage distribution system could have an impact not only on pupils' hydration, but also on pupil behaviour" - as they were likely to buy products outside school "before, during and after the school day".
Coca-Cola offers about 20 brands including carbonated and still, regular, low and no added sugar drinks, water, juice and juice-based drinks, sports and energy drinks and cordials.
It argues that low or no added sugar drinks should be included in official recommendations, along with low salt snacks, as "proven tools to tackle obesity".
The School Food Trust rejected that argument.