Does the van der Waals force not affect the alkali metal 's trend of decreasing melting points down the table?
Because, in the condensed phases, you don't have molecules of metallic elements.  You have, as a first approximation, a "rice pudding" structure where cations are embedded (like raisins) in a "pudding" of delocalized valence electrons (metallic bonding).  The main cohesive force in the condensed metals is then electrostatic attraction between the opposing charges of the cations and electrons.  In alkali metals where each atom breaks up into the same charge cation (+1 charge) and produces the same number of delocalized electrons (one per atom), this electrostatic attraction goes down with larger atoms.