>If we consider block + spring as our system then the the net work done by internal forces would be zero , So what is increasing the potential energy of the system then ?

See this is the whole point behind the harmonic oscillator , you don't need any 'external' to drive the object to keep it's oscillating behaviour. You give the harmonic oscillator a little push and, due to the nature of the set up, the force law is such that that the body keeps moving without ever stopping (in the ideal case).

As per 'what' is increasing the potential energy, you can say that the internal forces of the system are responsible for it. The internal forces do no work, but it needn't be that they can't convert PE and KE back and forth.

I think it may help to learn the distinction between gravitational potential and gravitational potential energy [see here](https://en.wikipedia.org/wiki/Gravitational_potential)