We consider the three fundamental one-loop Feynman diagrams of QED, viz. vertex correction, fermion self-energy and vacuum polarisation in the light-front gauge and discuss the equivalence of their standard covariant expressions with the light-front expressions obtained using light-cone time-ordered Hamiltonian perturbation theory. Although this issue has been considered by us and others previously, our emphasis in this article is on addressing the ambiguity regarding the correct form of the gauge boson propagator to be used in the light-front gauge. We generalise our earlier results and show, using an alternative method called the asymptotic method, how integrating over the light-front energy consistently in the covariant expression of each of the three one-loop corrections leads to the propagating as well as the instantaneous diagrams of the light-front theory. In doing so, we re-establish the necessity of using the correct form of gauge boson propagator.