If Littlefinger knows Tywin is dead, he knows that he can send one of his spies to the already existing sparrows. The faith don't have to be corrupt for this to work.
The sparrows infiltrate Littlefinger's brothel on their information and find the High Septon.
The High Septon demands justice for this outrage, but Littlefinger calculates that the crown won't risk angering the people by giving a corrupt religious leader with no bargaining position their support. What they do instead is back the sparrows .
Littlefinger may not know that Cersei would arm them, but just letting them hold sway over the people in King's Landing is more than enough to cause a great amount of civil unrest.
Now, once shit goes down, Littlefinger lets Polyvar know his game and Polyvar (being one of LF's spies and his brothel keeper) voluntarily turns on Loras, and inadvertently get Margaery imprisoned in the process.
Having Cersei imprisoned was a total accident, which is why her penance walk results in her freedom, and why Kevan is now back to fix things once the walk is over.
Having Margaery and Loras imprisoned is convenient for Littlefinger because it allows him to drive the Tyrells even further from the Lannisters while he bids for the north.
