Neutral points in an electrical circuit?

I have been told that potential in an electric circuit is defined as the work done in bringing a unit test positive charge to that point inside the circuit.

True, but you have to know where the point is in the circuit where the test positive charge starts. Then, the potential difference (voltage) between the two points in the electric circuit is the work required per unit charge to move the test charge between the two points.

Thus it satisfies the premise that potential at the positive terminal is greater and keeps decreasing as we move away from it.

True. When the positive charge moves away from the positive terminal of the battery its potential decreases and vice versa.

Near the negative terminal work done is negative thus potential is lower at that point.

As you move away from the positive terminal towards the negative terminal in the circuit the electric field does positive work converting electrical potential energy into kinetic energy (movement) of the charge. Then as the charge moves through the circuit it alternatively gives up kinetic energy to the circuit components while simultaneously regaining it from the field. It is the circuit components that do negative work on the charge taking the kinetic energy the charge gave up and either dissipates it as heat in resistors, or stores it as potential energy in the electric field of capacitors or as kinetic energy in the magnetic field of inductors. The net change in kinetic energy of the charge moving through the circuit is zero, which makes the current constant.

This seems logical and can be understood with the help of electric fields but following this assumption there must be a point in the circuit at which intensity of electric field due to both the terminals becomes 0, and thus potential at this point would become 0 like neutral points in a magnetic field. Is this true or did I go wrong somewhere?

In order for the electric field to be zero at some point in the circuit between the two battery terminals, the charges on the terminals would have to be of the same sign, i.e., both positive or both negative, as well as of the same magnitude. In that case the electric field at the midpoint between the terminals would be zero, but the electric potential would not be zero. The potential would either have two positive contributions if the charges were positive or two negative contributions if the charges were negative.

But obviously the charges on the battery terminals are not only equal in magnitude but are opposite in sign. The electric field vector points away from the positive terminal and towards the negative terminal, and the potential is zero only at the negative terminal.

Hope this helps.