Is the rear hub loose enough?
Lift the back end of the bike so the rear wheel is off the ground. Give the wheel a spin. The easiest way to do this is by gently pressing a pedal. It must turn smoothly without clicks or catches. If the bike has a freewheel that will make an even noise but the rear hub must be smooth. If there’s a problem with the brake open it to check the rear hub. Mudguards rubbing may be another source of distracting problems.