The 42-year-old had taken over the Kent outfit at the end of January but has now left in a move that has taken the club by surprise.
Drury won two of his eight games in charge of the Cannons, who were rock bottom when he arrived, but he hasn’t been able to change the fortunes of the ninth tier club.
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They sit 12 points from safety in the Southern Counties East Premier Division with six games remaining.
They are now looking for their fourth manager this season and facing successive relegations, just three years after reaching the Isthmian South East play-off final.
Drury, who made 65 appearances and scored twice for the Blues, has previously managed three other clubs based in Kent, including Folkestone Invicta, Whitstable Town and Margate.