  We describe a method to analyse inclined air showers produced by ultra high
energy cosmic rays using an analytical description of the muon densities. We
report the results obtained using data from inclined events
(60^{\circ}<\theta<80^{\circ}) recorded by the Haverah Park shower detector for
energies above 10^19 eV. Using mass independent knowledge of the UHECR spectrum
obtained from vertical air shower measurements and comparing the expected
horizontal shower rate to the reported measurements we show that above 10^19 eV
less than 48 % of the primary cosmic rays can be photons at the 95 % confidence
level and above 4 X 10^19 eV less than 50 % of the cosmic rays can be photonic
at the same confidence level. These limits place important constraints on some
models of the origin of ultra high-energy cosmic rays.
