Given the electric field is uniform, if we consider a plane perpendicular to electric field we can say that this plane is an equipotential surface(as equipotential surfaces are perpendicular to the electric field lines.)

Equipotential surface: A surface on which all points on the surface have the same electric potential.

That means by definition of potential difference (between two points) which is defined as work done in moving a unit test charge from one point to another point,

We can say that zero work is done in moving a unit test charge on this surface.

Let us assume that some charge is present in this region where electric field is uniform. Now due to this charge our test charge when introduced experiences a force (repulsive or attractive) due to which non-zero work needs to be done to move our test charge from one point to another.

And if non zero work is done that means the potential difference between these two points is finite (and not zero) and the surface can’t be considered as equipotential.

This is a contradiction to the fact that the surface is equipotential.

Therefore net charge in the region of uniform electric field is zero.