My question is if there is always equal and opposite voltage in an inductor against the applied voltage then how can the current flow in such a circuit?
The interesting point is that you probably have never queried the fact that there is a current in a circuit consisting of a cell and a resistor in which the voltage across the cell (its emf) is opposite to that of the voltage across the resistor?
In this example, the cell is a source of electrical energy (which is produced from chemical energy) and the resistor is a sink of electrical energy (which produces heat).
The fact that these two voltages add up to zero (Kirchhoff’s voltage law) is a statement of the law of conservation of energy in a form which is useful when considering electrical circuits.
At any instant of time the electrical power generated by the voltage supply is equal to the power dissipated as heat in the resistor.
In the case of an alternating voltage source and an inductor the law of conservation of energy still holds but sometimes, when the magnitude of the current is increasing, the voltage supply is the source of electrical energy and the inductor the sink with the energy stored in the magnetic field and at other times, when the magnitude of the current is decreasing, the voltage supply is the sink of electrical energy and the inductor the source with the energy obtained from the decreasing magnetic field.