Cross-sectional studies show that older people with better cognition tend to walk faster. Whether this association reflects an influence of fluid cognition upon walking speed, vice versa, a bidirectional relationship or the effect of common causes is unclear. We used linear mixed effects models to examine the dynamic relationship between usual walking speed and fluid cognition, as measured by executive function, verbal memory and processing speed, in 2,654 men and women aged 60 to over 90 years from the English Longitudinal Study of Ageing. There was a bidirectional relationship between walking speed and fluid cognition. After adjusting for age and sex, better performance on executive function, memory and processing speed was associated with less yearly decline in walking speed over the 6-year follow-up period; faster walking speed was associated with less yearly decline in each cognitive domain; and less yearly decline in each cognitive domain was associated with less yearly decline in walking speed. Effect sizes were small. After further adjustment for other covariates, effect sizes were attenuated but most remained statistically significant. We found some evidence that walking speed and the fluid cognitive domains of executive function and processing speed may change in parallel with increasing age. Investigation of the association between walking speed and cognition earlier in life is needed to better understand the origins of this relation and inform the development and timing of interventions.