A substantially different behaviour was observed between MgB2 wires produced either by in situ or ex situ processing after applying the recently developed technique of cold high pressure densification (or CHPD). In contrast to in situ wires, where densification at 1.5 GPa on binary and ternary alloyed in situ MgB2 wires causes an enhancement of mass density and a strong enhancement of Jc, ex situ wires up to 2 GPa show only a negligible enhancement of the MgB2 mass density, while a considerable enhancement of Jc is still observed. In both cases, this reflects an enhancement of grain connectivity, however in ex situ wires, the enhancement of Jc is connected to the partial disruption of the oxide layer around each MgB2 powder particle, in contrast to the enhancement of Jc in situ wires, which is correlated to a smaller void fraction and a larger contact area between neighbouring grains. It is well known that Jc of ex situ wires decreases after longer exposition times when exposed to air prior to annealing; after several months Jc falls to values ≤50% of the original value. After cold pressing, we have found that Jc of the same wire exceeded the original values, even after exposing the unreacted wire for >1 year to air. A lower electrical resistivity is measured on pressed ex situ MgB2 wires, which confirms the improvement of grain connectivity due to the breakage of the oxide layers. Thus, the application of high pressure at room temperature allows us to recover the values of Jc for ex situ wires even after they have been degraded either by low quality MgB2 precursors or by prolonged ageing of the already formed wire prior to the final heat treatment. The limits of the Jc enhancement in ex situ wires are discussed.