This paper proposes and analyses an algorithm to solve parametric nonlinear optimisation problems, where the target function is assumed to be convex and the parameter appear in a linear way in the equality constraints. The proposed algorithm is based on a predictor-corrector path-following approach in combination with sequential convex programming to compute solutions of the parametric nonlinear optimisation problems for a sequence of parameter values. The convergence of the proposed method is analysed for exact as well as for inexact derivative information. The optimal control of a hydro power plant serves as numerical example to illustrate the performance of the new approach.