We have observed neutral carbon, [CI], and isotopic carbon monoxide (C^18O 3-->2 and C^18O 2-->1) towards the nucleus of the starburst galaxy NGC 253. [CI] is bright and we derive a mean abundance ratio C^0/CO~0.5 across the central ~300 pc of the starburst. Observations of ^13CO, by Wall et al., indicate that the bulk of the molecular gas in the starburst region is hot (T~100K) and dense (<e1>n<~</e1>10^4 cm^-3). Our observations show that C^18O traces the smaller fraction of cold molecular gas and, thus, is a poor tracer of the column density of molecular gas in NGC 253. The effects of selective photodissociation on CO and its isotopomers means that it is unwise to use CO to derive reliable estimates of the intrinsic ^16O/^18O ratio in starburst nuclei. Standard models of photon-dominated regions (PDRs) can only account for about 5 per cent of the observed C^0 emission. As most of the molecular gas is at low visual extinction and is hot, the enhanced cosmic ray flux expected in the nucleus of NGC 253 should play little or no part in enhancing the carbon emission with respect to other PDR tracers and CO. The nature of the bulk of the molecular gas in NGC 253, and the size of the region (~300 pc), rules out time-dependent chemistry across the nucleus as the explanation for the large abundance of atomic carbon. The most plausible explanation for the brightness of [CI] emission is that the C/O elemental ratio is higher in NGC 253 than in the models with which we compare our observations. NGC 253 shows evidence for a dense torus of gas around the nucleus (R~50 pc) but does not have any inner Lindblad resonances. The most likely explanation for the existence of the torus is pressure confinement of the gas by a superwind.