The Gibbs-Bogoliubov (GB) inequality is used to evaluate the Helmholtz free energy of liquid alkali metals as a function of temperature. The structural contribution to the Helmholtz free energy is investigated by adopting a charged hard sphere fluid model. A well established single parametric local pseudopotential is applied to describe the electron-ion interaction along with five different local field correction functions viz; Hartree, Taylor, Ichimaru and Utsumi, Farid et al., and Sarkar et al., 6.2% to 51.15% of the influence on the Helmholtz free energy is concluded to be due to these local field correction functions with respect to the static Hartree dielectric function. Very good agreement with experimental results is achieved.