The Trouble With Mr. Bean - S1-E8
Trivia: Up until this episode we have never seen the driver of the blue Reliant that's always had the misfortune of running into Mr. Bean. In this episode that same car is parked in front of the dentist office which is then pushed back by Bean's car. It is possible then that the unseen driver could either be the woman with small child or the patient who leaves just before Bean meets the dentist.
Answer: Don't think it was an actual programme; more likely just sounds they recorded themselves.