Results are presented on the photoproduction of isolated prompt photons, inclusively and associated with jets, in the gamma p center of mass energy range 142 4.5 GeV. They are measured differentially as a function of E_T^gamma, E_T^jet, the pseudorapidities eta^gamma and eta^jet and estimators of the momentum fractions x_gamma and x_p of the incident photon and proton carried by the constituents participating in the hard process. In order to further investigate the underlying dynamics, the angular correlation between the prompt photon and the jet in the transverse plane is studied. Predictions by perturbative QCD calculations in next to leading order are about 30% below the inclusive prompt photon data after corrections for hadronisation a...