In this paper, we consider modified Galerkin and iterated modified Galerkin methods for solving a class of two point boundary value problems. The methods are applied after constructing the equivalent derivative dependent Fredholm-Hammerstein integral equations to the boundary value problem. Existence and convergence of the approximate solutions to the actual solution is discussed and the rates of convergence are obtained. Superconvergence results for the approximate and iterated approximate solutions of piecewise polynomial based modified Galerkin method in infinity norm are given. We have also established that iterated modified Galerkin approximation improves over the modified Galerkin solution. Numerical examples are presented to illustrate the theoretical results.