At lunchtime on 28 June cheese was flicked or thrown into Karan's face, the Daily Telegraph reported.
He later went to the school's office where allergy medicine is kept but staff were unable to help and called an ambulance.
Karan died in hospital less than two weeks later surrounded by his family.
A 13-year-old boy at the same school was arrested on suspicion of attempted murder on June 28 and has since been released on bail.
Amarjeet Cheema, 53, Karan's father, told the Evening Standard: "We were in hospital I had to watch him die, no parent should have to go through that.
"While he was in hospital we were fully concentrated on his condition.
"Now we want answers. How could this have happened?
""My son had allergies but he was very careful. He had an allergy to dairy products but was good at avoiding them.
"I don't how a piece of cheese hitting him could have killed him, it doesn't make any sense."
The School's head teacher, Dame Alice Hudson, said staff had tried to administer medication to the teenager before the ambulance arrived.
She said: "Karanbir Cheema, known as Karan, was a popular Year 8 student at the school.
"He had many friends who are devastated at his death, as are the staff.
"He was a bright and keen student who excelled in maths."