The big food companies, on the defensive for fostering obesity in young people, are being pressured by the government to stump up cash for sports facilities, according to a cabinet-level leak.

The unspoken warning from ministers is that the companies need to improve their image by providing cash for sport or political pressure will force the government to clamp down on their advertising to children.

The issue of advertising is being examined by ministers, with opinion sharply divided.

Tessa Jowell, the culture and sport secretary, says there will be no explicit deal in which the food companies provide cash for sport in return for unregulated advertising. The leaked papers show the government is proposing a business-sponsored national foundation for sport, to build sports centres, gyms, football pitches and tennis courts.

The government provides £700m for sports facilities in schools. But a Downing Street strategy unit report suggested that lottery funds for sports may decline and too much cash is being spent on a few large prestigious contracts.

The leaked paper, a discussion on the summer spending review, suggested that for every £3 of private investment, the government could contribute £1.

Representatives of the food industry are to meet ministers this week. Their enthusiasm for the plan will depend on the extent to which it is voluntary.