One leading candidate theory of high-temperature superconductivity in the copper oxide systems is the interlayer tunnelling (ILT) mechanism(1). In this model, superconductivity is created by tunnelling of electron pairs between the copper oxide planes-contrasting with other models in which superconductivity first arises by electron pairing within each plane. The ILT model predicts that the superconducting condensation energy is approximately equal to the gain in kinetic energy of the electron pairs due to tunnelling. Both these energies can be determined independently(2-4), providing a quantitative test of the model. The gain in kinetic energy of the electron pairs is related to the interlayer plasma frequency, omega(J), of electron pair oscillations, which can be measured using infrared spectroscopy. Direct imaging of magnetic flux vortices also provides a test(5), which is performed here on the same samples. In the high-temperature superconductor Tl2Ba2CuO6, both the sample-averaging optical probe and the local vortex imaging give a consistent value of omega(J) approximate to 28 cm(-1) which, when combined with the condensation energy produces a discrepancy of at least an order of magnitude with deductions based on the ILT model.