Some studies have identified declines in mental health during the Coronavirus Disease 2019 (COVID-19) pandemic in different age groups, including older people. As anxiety and depression are common neuropsychiatric symptoms among people with cognitive impairment, the mental health experiences of older people during the pandemic should take cognitive function into consideration, along with assessments made prior to the pandemic. This study addresses evidence gaps to test whether changes in depression and anxiety among older people through the COVID-19 pandemic were associated with cognitive impairment. It also investigates whether associations varied according to key sources of sociodemographic inequality. Using data from the English Longitudinal Study of Ageing (ELSA) collected from 2018/2019 to November/December 2020, we estimated changes in depression and anxiety for people aged 50+ in England across 3 cognitive function groups: no impairment, mild cognitive impairment, and dementia. Conditional growth curve models were estimated for continuous measures over 3 time points (N = 5,286), with mixed-effects logistic regression used for binary measures. All models adjusted for demographics (age, gender, ethnicity, and cohabiting partnership), socioeconomics (education, wealth, and employment status), geography (urban/rural and English region), and health (self-rated and the presence of multimorbidity). We found that depression (measured with CES-D score) worsened from 2018/2019 to November/December 2020 for people with mild cognitive impairment (1.39 (95% CI: 1.29 to 1.49) to 2.16 (2.02 to 2.30)) or no impairment (1.17 (95%CI: 1.12 to 1.22) to 2.03 (1.96 to 2.10)). Anxiety, using a single-item rating of 0 to 10 also worsened among those with mild cognitive impairment (2.48 (2.30 to 2.66) to 3.14 (2.95 to 3.33)) or no impairment (2.20 (2.11 to 2.28) to 2.85 (2.77 to 2.95)). No statistically significant increases were found for those with dementia. Using a clinical cutoff for likely depression (CES-D ≥4), we found statistically significant increases in the probability of depression between 2018/2019 and November/December 2020 for those with no impairment (0.110 (0.099 to 0.120) to 0.206 (0.191 to 0.222)) and mild impairment (0.139 (0.120 to 0.159) to 0.234 (0.204 to 0.263)). We also found that differences according to cognitive function that existed before the pandemic were no longer present by June/July 2020, and there were no statistically significant differences in depression or anxiety among cognitive groups in November/December 2020. Wealth and education appeared to be stronger drivers for depression and anxiety, respectively, than cognitive impairment. For example, those with no impairment in the richest two-thirds scored 1.76 (1.69 to 1.82) for depression in June/July, compared to 2.01 (1.91 to 2.12) for those with no impairment in the poorest third and 2.03 (1.87 to 2.19) for those with impairment in the poorest third. Results may be limited by the small number of people with dementia and are generalizable only to people living in the community, not to those in institutional care settings. Our findings suggest a convergence in mental health across cognitive function groups during the pandemic. This suggests mental health services will need to meet an increased demand from older adults, especially those not living with cognitive impairment. Further, with little significant change among those with dementia, their existing need for support will remain; policymakers and care practitioners should ensure this group continues to have equitable access to mental health support.