Kingsman creator Mark Millar has helped clarify this for people now by taking to Twitter to explain the difference. As he says, the prequel, previously given the title Kingsman: The Great Game, is about the beginnings of the Kingsman organization a hundred years ago and so obviously, it wouldn’t find a place for Eggsy.
“People seem awfully confused by this. The Kingsman movie Matthew is shooting in the New Year is a prequel set at the beginning of the organisation in 1918 as reported a while back. Kingsman 3 comes later.