A large acceptance polarimeter has been designed to measure recoil polarisation in pseudoscalar (Jπ=0−) meson photoproduction reactions. The device was installed at the MAMI facility at the Institut für Kernphysik in Mainz, Germany. A racetrack microtron provided a longitudinally polarised 1.5 GeV electron beam, which impinged on a 12 μm copper radiator, producing a beam of circularly polarised Bremsstrahlung photons with energies between 400-1400 MeV. The electrons were then momentum analysed in the Glasgow Photon Tagging Spectrometer to tag the photon energy with a resolution of ~4 MeV. The photons were incident on a liquid hydrogen target, and the reaction products were detected using the Crystal Ball and TAPS detectors. The beam-recoil polarisation observable Cx, which describes the fraction of circular polarisation transferred from the photon beam to the recoiling nucleon, was measured in the reactions γp→pπ0 and γp→pη from data taken in September-October 2008. The results for π0 production give a significant expansion of the world data set and are shown to be consistent with the few previous measurements taken at Jefferson Lab, USA, while the results for the η channel are a world first. The observed values for Cx are compared to the current solutions from the two leading partial wave analyses, SAID and MAID, with wide angular coverage up to a photon beam energy of 1400 MeV. Significant discrepancies in the prediction of Cx can be resolved by the new data.