Why does the national grid use different voltages?

When transferring power over distance, the designer of the power line selects a voltage that optimizes the amount of power that is transferred, ie, minimizes the amount of power that is lost. There are tradeoffs in the selection of a voltage for a transmission line, as there are in almost any aspect of design. Too low a voltage (which requires a higher current) results in increased resistive losses in the lines, or you have to use heaver wire, which increases costs, not just of the wire, but of the stronger towers needed to support the wire. Too high a voltage leads to corona discharge losses and losses due to capacitance between lines and lines to ground. In addition, an AC voltage can be easily changed from one voltage to another with very small loss in power. So bottom line, each distribution line has a voltage selected to be optimum for that line. Connections between lines of different voltages are easily done via Transformers.
wire has inherent resistance. Power lost in this resistance is equivalent to P = I*I*R, where I is the current. Reducing the amount of current will reduce the inherent losses due to transporting power long distances. Power is equivalent to P = V*I; So, if we reduce the current, we must increase the voltage to maintain the same amount of power.
Simply put, it is much more efficient. There is less loss transmitting the same amount of power down a line using high voltage rather than a lower voltage. Let's look and see why. Consider that the transmission lines have resistive properties (in ohms/foot). These represent a fixed loss; we can't get around them. We start with Ohm's Law: V=IR, and the definition of Power: P=VI. Substituting IR for V, we see that P=I²R. What this tells us is that the amount of power lost in the lines is equal to the square of the current flowing through the lines, times the resistance of the lines. The amount of power transmitted is constant, and the resistance in the lines is constant. So, if we double the voltage, the current is cut in half, and the losses are cut in quarter. The simple mathematics drives (dictates) that we use as high a voltage as is practical to transmit power over long lines to minimize the loss.