Two-dimensional (2D) materials such as graphene and transition-metal dichalcogenides reveal the electronic phases that emerge when a bulk crystal is reduced to a monolayer(1-4). Transition-metal oxide perovskites host a variety of correlated electronic phases(5-12), so similar behaviour in monolayer materials based on transition-metal oxide perovskites would open the door to a rich spectrum of exotic 2D correlated phases that have not yet been explored. Here we report the fabrication of freestanding perovskite films with high crystalline quality almost down to a single unit cell. Using a recently developed method based on water-soluble Sr3Al2O6 as the sacrificial buffer layer(13,14) we synthesize freestanding SrTiO3 and BiFeO3 ultrathin films by reactive molecular beam epitaxy and transfer them to diverse substrates, in particular crystalline silicon wafers and holey carbon films. We find that freestanding BiFeO3 films exhibit unexpected and giant tetragonality and polarization when approaching the 2D limit. Our results demonstrate the absence of a critical thickness for stabilizing the crystalline order in the freestanding ultrathin oxide films. The ability to synthesize and transfer crystalline freestanding perovskite films without any thickness limitation onto any desired substrate creates opportunities for research into 2D correlated phases and interfacial phenomena that have not previously been technically possible.