In Chapter 45 of AGOT Eddard Stark had this conversation with Cersei, while Robert was away from King's Landing on a hunt:
“For a start,” said Ned, “I do not kill children. You would do well to listen, my lady. I shall say this only once. When the king returns from his hunt, I intend to lay the truth before him. You must be gone by then.”
But later on, he has this conversation with Varys:
Varys “If there was one soul in King’s Landing who was truly desperate to keep Robert Baratheon alive, it was me.” He sighed. “For fifteen years I protected him from his enemies, but I could not protect him from his friends. What strange fit of madness led you to tell the queen that you had learned the truth of Joffrey’s birth?”
Ned “The madness of mercy,” Ned admitted.
Varys“Oh, indeed. Cersei gave him the wineskins, and told him it was Robert’s favorite vintage.” The eunuch shrugged. “A hunter lives a perilous life. If the boar had not done for Robert, it would have been a fall from a horse, the bite of a wood adder, an arrow gone astray … the forest is the abbatoir of the gods. It was not wine that killed the king. It was your mercy.”
We find out later that
Lancel Lannister, King Robert's squire, gave him the wineskins
But how could the queen have given this order when the King - and presumably his squire - were already away from the city on the hunt?