Results are presented on the photoproduction of isolated prompt photons, inclusively and associated with jets, in the γp center of mass energy range 142 < W < 266 GeV. The cross sections are measured for the transverse momentum range of the photons 5 < Eγ T < 10 GeV and for associated jets with Ejet T > 4.5 GeV. They are measured differentially as a function of Eγ T,Ejet T , the pseudorapidities ηγ and ηjet and estimators of the momentum fractions xγ and xp 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 and multiple interactions, but are in reasonable agreement with the results for prompt photons associated with jets. Comparisons with the predictions of the event generators PYTHIA and HERWIG are also presented.