A laterally adjustable rail clip fastening means is provided by the present invention for securing a resilient rail clip such as a Pandrol clip to a direct fixation rail mounting assembly, and, in turn, into engagement with a rail. The rail clip fastening means includes a pair of sections of rigid material formed with a curved portion at one end which receive and securely hold a resilient rail clip in engagement with the rail. Each of the sections are engageable with a disc means rotatably disposed within the top plate of the rail mounting assembly on opposite sides of the rail. The disc means are rotatable to move the sections laterally along the top plate, and include locking means to independently lock such sections into a position against the rail for preventing lateral movement thereof in cooperation with the resilient rail clips.