We present a detailed study of the radiative potential method [V. V. Flambaum and J. S. M. Ginges, Phys. Rev. A 72, 052115 (2005), 10.1103/PhysRevA.72.052115], which enables the accurate inclusion of quantum electrodynamics (QED) radiative corrections in a simple manner in atoms and ions over the range 10 ≤Z ≤120 , where Z is the nuclear charge. Calculations are performed for binding energy shifts to the lowest valence s , p , and d waves over the series of alkali-metal atoms Na to E119. The high accuracy of the radiative potential method is demonstrated by comparison with rigorous QED calculations in frozen atomic potentials, with deviations on the level of 1%. The many-body effects of core relaxation and second- and higher-order perturbation theory on the interaction of the valence electron with the core are calculated. The inclusion of many-body effects tends to increase the size of the shifts, with the enhancement particularly significant for d waves; for K to E119, the self-energy shifts for d waves are only an order of magnitude smaller than the s -wave shifts. It is shown that taking into account many-body effects is essential for an accurate description of the Lamb shift.