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Leo I is considered one of the youngest dwarf spheroidals (dSph) in the Local Group. Its isolation, extended star formation history (SFH), and recent perigalacticon passage (~1 Gyr ago) make Leo~I one of the most interesting nearby stellar systems. Here, we analyse deep photometric Hubble Space Telescope data via colour-magnitude diagram fitting techniques to study its global and radially-resolved SFH. We find global star formation enhancements in Leo I ~13, 5.5, 2.0, and 1.0 Gyr ago, after which it was substantially quenched. Within the context of previous works focused on Leo I, we interpret the most ancient and the youngest ones as being linked to an early formation (surviving reionisation) and the latest perigalacticon passage (transition from dIrr to dSph), respectively. We clearly identify the presence of very metal poor stars ([Fe/H]~-2) ageing ~5-6 and ~13 Gyr old. We speculate with the possibility that this metal-poor population in Leo I is related to the merging with a low mass system (possibly an ultra-faint dwarf). This event would have triggered star formation (peak of star formation ~5.5 Gyr ago) and accumulated old, metal poor stars from the accreted system in LeoI. Some of the stars born during this event would also form from accreted gas of low-metallicity (giving rise to the 5-6 Gyr low-metallicity tail). Given the intensity and extension of the 2.0 Gyr burst, we hypothesise that this enhancement could also have an external origin. Despite the quenching of star formation around 1 Gyr ago (most probably induced by ram pressure stripping with the Milky Way halo at pericentre), we report the existence of stars as young as 300-500 Myr. We also distinguish two clear spatial regions: the inner ~190 pc presents an homogeneous stellar content (size of the gaseous star forming disc in LeoI from ~4.5 to 1 Gyr ago), whereas the outer regions display a clear positive age gradient.