  Exclusive $J/\psi$ and $\psi(2S)$ vector meson production has been observed
in the dimuon channel using the LHCb detector. The cross-section times
branching fractions to two muons with pseudorapidities between 2.0 and 4.5 are
measured to be $ \sigma_{pp\rightarrow J/\psi (\rightarrow \mu^{+} \mu^{-})}
(2.0 <\eta_{\mu^{\pm}}< 4.5) = 307 \pm 21 \pm 36 \text{pb},
\sigma_{pp\rightarrow \psi(2S) (\rightarrow \mu^{+} \mu^{-})} (2.0
<\eta_{\mu^{\pm}}< 4.5) = 7.8 \pm 1.3 \pm 1.0 \text{pb}, $ where the first
uncertainties are statistical and the second are systematic. The measurements
are found to be in good agreement with results from previous experiments and
theoretical predictions. The $J/\psi$ photoproduction cross-section has been
measured as a function of the photon-proton centre-of-mass energy. The results
are consistent with measurements obtained at HERA and confirm a similar power
law behaviour for the photoproduction cross-section.
