There are four Acts, or chapters, as you play through the game. The end of one act and the start of the next is loosely triggered by some action that you take.
You are not outright forced to complete one act before another opens. It is possible to have, for example, acts two and three both in progress at the same time, even if you have not fully completed act two.
Act I
The first act is almost just a tutorial that lets new players learn the game and grasp the basic mechanics.
It is worth noting that at points, at least on Beginner and Easy level, you can simply pass time by clicking the End Turn icon; meanwhile gaining cash, food and experience for your knights.
Act II
This chapter is where the game opens up properly. You get access to Strongholds with the Boroughs, Chancellery and the Upgrades available.
You also start getting random quests and disasters which can greatly affect the flow of the game for you depending on how you play.
Act III
The third chapter appears to start with your conquest of the second of London or Viroconium. This is a tentative suggestion based on my limited play time so far.
Act IV
???