An SPTC survey of 1,151 individuals in 92 schools, published today (Friday), found that 56 per cent wanted current procedures tightened - but only 15 per cent backed an all-out ban.
Some parents thought a selective ban might be a better option, while others suggested advertising could have a positive effect - to promote healthy food, for example.
There was particular criticism of companies that used "pester power" to persuade parents to buy products or use certain shops, with Tesco and Funny Bones singled out.
National guidelines to regulate business advertising and sponsorship in schools did not find much favour, with some parents saying that this was best left to the headteacher's discretion.
The SPTC says: "There is considerable unhappiness about multinationals, particularly the food giants when their products are seen as contrary to current efforts to promote healthy eating."