Downriver from Richmond Bridge, about a quarter of a mile along the towpath past Richmond's handsome period riverfront buildings, is rather boring Twickenham Bridge, a fast unpleasant road bridge dating from the 1930s. Both sides have shared pedestrian/cycle paths.
You have three options for accessing Twickenham Bridge: 1. Use the stairs both sides – four brief but steep flights. 2. Go by road, a ten-minute detour away from the river on both banks to join the bridge (from Richmond involves a short-cut through a car park) 3. Skip Twickenham Bridge and Richmond Lock footbridge (which also involves a few steps) and just carry on along the south bank.
Confusingly, the south bank is the north bank here, and vice-versa, because of the way the river bends. So the two sides are sometimes called the Middlesex and Surrey banks, after the two fictional counties that play cricket.
Cross the bridge to the north (ie south) side and find your way back south (ie north) to the riverside lane on the north (ie south) side. It's only a few hundred metres (ie yards) to Richmond Lock footbridge.