Cold high pressure densification was found to substantially enhance the critical current density of binary in situ Fe/MgB2 wires. A wire densified at 1.85 GPa exhibited at 20 K and 5 T an increase of Jc by 300% with respect to same wire without the application of pressure. At 4.2 K and 10 T, Jc was found to be increased by 53%. The decrease of the electrical resistance for densified wires reflects an improved connectivity. The values of Birr at 4.2 and 20 K were enhanced up to 0.7 T for densified wires. After applying pressures up to 6.5 GPa at 300 K, the relative mass density dm of the unreacted (B+Mg) mixture inside the filament increased up to 96% of the theoretical density. This corresponds to a relative mass density df in the reacted MgB2 filaments of 73%. A quantitative correlation between filament mass density and critical current density was established.