  The total cross section for the photoproduction process with a leading proton
in the final state has been measured at gamma p centre-of-mass energies W of
91, 181 and 231 GeV. The measured cross sections apply to the kinematic range
with the transverse momentum of the scattered proton restricted to p_Tproton <=
0.2 GeV and 0.68 <= z <= 0.88, where z = E_p'/E_p is the scattered proton
energy normalised to the beam energy. The cross section dsigma_(gamma p ->
Xp')(W,z)/dz is observed to be independent of W and z within the measurement
errors and amounts to 8.05 +- 0.06 stat +- 0.89 syst mub on average. The data
are well described by a Triple Regge model in which the process is mediated by
a mixture of exchanges with an effective Regge trajectory of intercept
alpha_i(0)=0.33 +- 0.04 stat +- 0.04 syst. The total cross section for the
interaction of the photon with this mixture (gamma alpha_i -> X) can be
described by an effective trajectory of intercept alpha_k(0)=0.99 +- 0.01 stat
+- 0.05 syst. Predictions based on previous triple Regge analyses of pp-> pX
data assuming vertex factorisation are broadly consistent with the gamma p
data. The measured cross sections are compared with deep inelastic scattering
leading proton data in the same region of z and pT_proton for photon virtuality
Q^2 > 2.5 GeV^2. The ratio of the cross section for leading proton production
to the total cross section is found to rise with Q^2.
