Seed, core, and finely chop tomatoes. Measure 3 1/2 cups chopped tomatoes; place in a 6- to 8-quart stainless-steel, enamel, or nonstick heavy pot. Bring to boiling, stirring occasionally; reduce heat. Simmer, covered, for 10 minutes. Measure 3 1/3 cups tomatoes; return to pot. Stir in lemon juice and basil.
In a small bowl combine 1/4 cup of the sugar and the pectin; stir into tomato mixture. Bring to a full rolling boil, stirring constantly. Stir in the remaining 2 3/4 cups sugar. Return to a full rolling boil, stirring constantly. Boil hard for 1 minute, stirring constantly. Remove from heat and quickly skim off foam with a metal spoon.
Ladle hot jam into hot sterilized 250ml jars, leaving a 1cm headspace and seal while hot.