Why aren't people allowed to leave King's Landing?

Question

In A Game of Thrones, one of Arya's chapters towards the end of the novel talks about how she couldn't leave King's Landing. At first, I thought this was because guards would be actively looking for her due to all the craziness happening with

King Robert's death and her father being accused of treason.

After reading on, Arya goes on to say that no one is permitted to leave King's Landing. Apparently, people are allowed in but no one is allowed out.

Why wouldn't people be allowed to leave King's Landing? In the same vein, if tensions are rising, why are people welcomed into the city to begin with?

Answer 1

This is the only reference I could find to what you're talking about, and it makes it pretty clear that people are allowed to leave King's Landing, but only by two of the seven gates to allow for efficient searching:

leaving King’s Landing was not so easy as she had hoped. ...

Every day since her escape from the Red Keep, Arya had visited each of the seven city gates in turn. The Dragon Gate, the Lion Gate, and the Old Gate were closed and barred. The Mud Gate and the Gate of the Gods were open, but only to those who wanted to enter the city; the guards let no one out. Those who were allowed to leave left by the King’s Gate or the Iron Gate, but Lannister men-at-arms in crimson cloaks and lion-crested helms manned the guard posts there. Spying down from the roof of an inn by the King’s Gate, Arya saw them searching wagons and carriages, forcing riders to open their saddlebags, and questioning everyone who tried to pass on foot.
_{A Game of Thrones - Arya V}

Answer 2

During a coup d'etat it is vital to keep physical control of important people. Many will attempt to flee from the fighting and to avoid being trapped. As is noted later, certain people became hostages, like the Redwyne twins. It is in the Lannister's best interest to make sure they not allow people to escape their control.