  We determine the ground state and first excited state masses of singly and
doubly charmed spin 1/2 and 3/2 baryons with positive and negative parity.
Configurations with $N_f=2+1$ non-perturbatively improved Wilson-clover
fermions were employed, with the same quark action also being used for the
valence quarks, including the charm. The spectrum is calculated for pion masses
in the range $M_\pi \sim 259-460$ MeV at a lattice spacing $a\sim 0.075$ fm.
Finite volume effects are studied comparing lattices with two different linear
spatial extents ($1.8\,{\rm fm}$ and $2.4\,{\rm fm}$). The physical point is
approached from the SU(3) limit keeping the flavour averaged light quark mass
fixed. The baryon masses are extrapolated using expansions in the strange-light
quark mass difference. Most particles fall into the expected SU(3) multiplets
with well constrained extrapolations, the exceptions having a possibly more
complex internal structure. Overall agreement is found with experiment for the
masses and splittings of the singly charmed baryons. As part of the calculation
an analysis of the lower lying charmonium, $D$ and $D_s$ spectra was performed
in order to assess discretisation errors. The gross spectra are reproduced,
including the $D^*_{s0}$, $D_{s1}$ and $D_1$ mesons, while at this single
lattice spacing hyperfine splittings come out $10-20$ MeV too low.
