  We present the first measurements of the muon-induced neutron flux at the
Boulby Underground Laboratory. The experiment was carried out with an 0.73
tonne liquid scintillator that also served as an anticoincidence system for the
ZEPLIN-II direct dark matter search. The experimental method exploited the
delayed coincidences between high-energy muon signals and gamma-rays from
radiative neutron capture on hydrogen or other elements. The muon-induced
neutron rate, defined as the average number of detected neutrons per detected
muon, was measured as $0.079 \pm 0.003$ (stat.) neutrons/muon using
neutron-capture signals above 0.55 MeV in a time window of 40-190 $\mu$s after
the muon trigger. Accurate Monte Carlo simulations of the neutron production,
transport and detection in a precisely modeled laboratory and experimental
setup using the GEANT4 toolkit gave a result 1.8 times higher than the measured
value. The difference greatly exceeds all statistical and systematic
uncertainties. As the vast majority of neutrons detected in the current setup
were produced in lead we evaluated from our measurements the neutron yield in
lead as $(1.31 \pm 0.06) \times 10^{-3}$ neutrons/muon/(g/cm$^2$) for a mean
muon energy of about 260 GeV.
