Burning might reduce it to some degree, but I don't think it will totally eradicate the problem. You did not indicate how you grew them, but staking or tellising the plants so there is good air circulation around them helps. Avoid watering the leaves, particularly in the afternoon/evening as they don't dry off as quickly as earlier in the day. Our recommendation is to rotate the crops so that you don't have the same crop in the same location for at least 3 years. While you don't want to use fungicides, various tomato fungal diseases can be managed with good cultural practices.