UNLABELLED: To develop healthy ageing interventions, longitudinal associations between objectively assessed physical behaviours and physical function need to be better understood. We assessed associations between accelerometer-assessed total physical activity (PA), moderate-to-vigorous physical activity (MVPA), light physical activity (LPA), sedentary time and prolonged sedentary bout time, and clinically assessed physical function (grip strength, usual walking speed (UWS), chair stand speed) at two time-points in 3188 participants (≥ 60 years) of the EPIC-Norfolk study. Bidirectional associations were assessed using multivariable linear regression. Over an average of 6.1 years, baseline physical behaviours (greater total PA, MVPA and LPA, and less sedentary time) were associated with better subsequent walking and chair stand speed. Better baseline physical function was associated with better follow-up physical behaviours. There were no bidirectional associations between changes in physical behaviours and grip strength. Improvements in UWS were associated with improvements in all physical behaviours. Improvements in chair stand speed were associated with improvements in total PA, MVPA, and sedentary bout time. Improvements in physical behaviours were associated with improvements in UWS (3.1 cm/s/yr per 100 cpm/yr total PA, 3.6 cm/s/yr per hr/day/yr MVPA, 2.5 cm/s/yr per hr/day/yr LPA, - 2.9 cm/s/yr per hour/day/yr sedentary time, and - 1.6 cm/s/yr per hr/day/yr prolonged sedentary bout time). Only improvements in total PA, MVPA and sedentary bout time were associated with improvements in chair stand speed. In conclusion, we found bidirectional associations between changes in some physical behaviours and physical function and between baseline physical behaviours and subsequent physical function, highlighting the importance of considering the full range of physical behaviours to promote healthy ageing. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10433-022-00733-y.