The growing body of experimental evidence(1-7) for the existence of complex textures of charges and spins in the high-temperature superconductors has drawn attention to the so-called ＇stripe-phase＇ model(8-12) as a possible basis for the mechanism of superconductivity in these materials. Such observations have until now been restricted to systems where the texture dynamics are slow or suppressed altogether, and do not include the important case of YBa2Cu3O7-delta. It seems likely that the dynamic behaviour of stripes(12,13), which has been suggested to undergo several phase transitions as a function of temperature(12), should also be reflected in the lattice properties of the host materials, and this forms the motivation for our present experiments. Specifically, we use MeV helium ion channelling, an ultrafast real-space probe of atomic displacements (with sub-picometre resolution), to probe incoherent lattice fluctuations in YBa2Cu3O7-delta as a function of temperature and oxygen doping. We detect lattice fluctuations that are larger than the expected thermal vibration component, and which show anomalies characteristic of the phase transitions anticipated for a dynamic stripe phase. Comparison of our lattice results with single-particle-tunnelling and photoemission data highlights the importance of spin-charge separation phenomena in the copper oxide superconductors.