The procedural deficit hypothesis claims that impaired procedural learning is a causal risk factor for developmental dyslexia and developmental language disorder. We investigated the relationships between measures of basic cognitive processes (declarative learning, procedural learning and attention) and measures of attainment (reading, grammar and arithmetic) in a large sample of 7- and 8-year-old children. A latent variable path model showed that verbal declarative memory skills predicted attainment but were not significantly related to attention. Procedural learning was only weakly related to measures of attainment and attention assessed during the procedural learning task accounted entirely for its relationship with measures of attainment. Our results challenge the procedural deficit hypothesis of reading and language disorders, but suggest that attentional skills (rather than procedural learning ability per se) may be an important predictor of reading, arithmetic and grammatical skills.