In the model of hole superconductivity, the pairing interaction enhances the mobility of the carriers. This gives rise to an additional contribution to the London kernel besides the one that is usually considered arising from the single-particle mobility. Thus, the penetration depth in a system described by this model will be shorter than what would be expected from estimates of the carrier effective mass in the normal state. We calculate the London penetration depth and examine its behavior for parameters believed to be appropriate to the high-${\mathit{T}}_{\mathit{c}}$ oxide superconductors. Our results interpolate smoothly between weak- and strong-coupling regimes. The contribution to the kernel from the pairing interaction becomes dominant in the strong-coupling limit, which within this model is achieved for low density of carriers. We also calculate within the framework of Ginzburg-Landau (GL) theory the GL coherence length and the upper critical field. The zero-temperature GL coherence length is not directly related to the average size of the pair wave function, as is usually the case, when the effect of the pairing interaction on the mobility is taken into account, and can be substantially larger. The relevance of these results to the interpretation of experimental data in high-${\mathit{T}}_{\mathit{c}}$ oxides is discussed.