Photoproduction events which have two or more jets have been studied in the Wγp range 135 GeV < Wγp < 280 GeV with the ZEUS detector at HERA. A class of events is observed with little hadronic activity between the jets. The jets are separated by pseudorapidity intervals (Δη) of up to four units and have transverse energies greater than 6 GeV. A gap is defined as the absence between the jets of particles with transverse energy greater than 300 MeV. The fraction of events containing a gap is measured as a function of Δη. It decreases exponentially as expected for processes in which colour is exchanged between the jets, up to a value of Δη ∼ 3, then reaches a constant value of about 0.1. The excess above the exponential fall-off can be interpreted as evidence for hard diffractive scattering via a strongly interacting colour singlet object.