People with cognitive impairments show deficits during physical performances such as gait, in particular during cognitively challenging conditions (i.e. dual‐task gait DTG). However, it is unclear if people at risk of dementia, such as those with subjective memory complaints (SMC), also display gait and central deficits associated with DTG. In this study, we investigated the effects of single‐ and dual‐task gait (STG and DTG), on left prefrontal cortex (PFC) activation in elderly people with subjective memory complaints (SMC) and Dementia. A total of 58 older adults (aged 65–94 years; 26 Healthy; 23 SMC; 9 Dementia) were recruited. Gait spatiotemporal characteristics (i.e. stride velocity and length) were assessed using an instrumented walkway during STG and DTG. Single‐channel functional near‐infrared spectroscopy over the left PFC was used to measure changes in oxyhaemoglobin (O2Hb) during gait. Stride velocity and length during STG (all p < .05) and DTG (all p < .000) were significantly impaired in people with Dementia compared to Healthy and SMC individuals. No differences were observed between Healthy and SMC. For STG, a greater increase in O2Hb (p < .05) was observed in those with Dementia compared to the Healthy and SMC, while no differences were observed between Healthy and SMC. A significant increase and decline in O2Hb was observed during DTG in the SMC and Dementia groups, respectively, compared to Healthy. Our findings indicate an altered pattern of cerebral haemodynamic response of the left PFC in DTG in people with SMC and Dementia, which may suggest that central changes precede functional impairments in people with SMC. No difference in single‐ and dual‐task gait (STG/DTG) was observed between controls and participants with subjective memory complaints (SMC). Participants with Dementia showed lower STG/DTG performance compared to controls and SMC. Participants with Dementia had greater left prefrontal cortex (PFC) activation during STG compared to controls and SMC. DTG resulted in higher and lower left PFC activation in SMC and Dementia, respectively, compared to controls.