Every city cyclist knows that whenever a vehicle overtakes the cyclist will catch up and pass them. Close overtaking by vehicles and then cutting in is what puts people off cycling and endangers them.
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The average speed of cars in cities is around 8mph (and getting slower year by year); cyclists average over 13mph. This is why vehicles overtaking cyclists is ultimately pointless. This would require no extra costs as cycle lanes are already in place, and would encourage more people to cycle as they would have preference on our roads.