Yes, customers can bring a pushchair/buggy with them onto one of the pods at the London Eye. It needs to be fully closed or folded before joining the boarding queue, remain closed throughout the experience including at the entrance/exit ramps, and should only be opened once out of the attraction.
Alternatively, there are left luggage facilities in the London Eye Ticket Office where ticket holders can leave their pushchair/buggy free of charge. These must be collected by 7pm.