I have read that since the magnetic force acting on moving charge is always perpendicular to the velocity of moving charge,...
To clear your mind I want to rephrase your statement and then tell you about Lorentz force.
Under the influence of a magnetic field a moving - not parallel to this field - charge gets deflected in a plane which is perpendicular to both the direction of the electrons movement and the direction of the magnetic field. (Note that the text between the hyphens “-“ is not necessary because in the case of the same directions of the magnetic field and the electrons movement the plane between them is zero.)
The phenomenon of this deflection is called the Lorentz force.
... the field is not doing any work on the charge.
To explained this phenomenon first one has to recognize that the charge gets deflected permanently. Telling you this you perhaps can conclude that the charge will moves in a circle. But carrying out the experiment with electrons in a Bubble chamber you will observe that the electron moves in a spiral path until in comes to rest.
Furthermore the charge loses permanently kinetic energy and this energy loss is realized in the form of emission of photons from the electron.
The next paragraph is a little bit tricky. Magnetic fields don’t interact with the electric field of a charge. So how the deflection happens? Please realize that the electron has not only an electric field, it has a permanent magnetic dipole too.
Moving into an external magnetic field the electrons magnetic dipole gets aligned and the electrons gets a little bit deflected. This deflection is an acceleration and as you know an acceleration of a charge is accompanied by the emission of electromagnetic radiation (photons). By this emission the electron gets disaligned again and the process starts again, but this time on a lower energy level until the kinetic energy is exhausted.
The magnetic field works like spring. You can do the Lorentz force experiment with an electromagnet as well as with a permanent magnet. The permanent magnet will have the same strength before and after the experiment.The electrons temporarely and periodically influence the shape of the external magnetic field and the external magnetic field align temporarily and periodic the electrons.
Does a force perpendicular to the direction of movement not do work?
Driving your bicycle and coming under the influence of a heavy crosswind you very fast will realize that this perpendicular force will do work. For the Lorentz force the emitted photons do the work. The magnetic field is the catalyst only.