Quarter the tomatoes and remove the core. Peel and coarsely chop the onions. Peel the apples, cut into quarters, and remove the core. Peel and finely dice the ginger. Peel and coarsely chop the oranges.
Bring the tomatoes, onions, apples, ginger, oranges, vinegar, sugar, and salt to a boil. Cover and simmer for 1 hour, until the mixture has a jam-like consistency. Fill the prepared screw-top jars to the brim with the chutney, seal tightly, and cool completely.