Powell Road resident and mum Kelly Purvor, 29, said she was 'disgusted' after seeing NHS staff engaged in a 'sex act' in a parked car outside her home.
She called the police, who traced the driver of the car and quizzed him, but ended up taking no action due to lack of evidence after he denied having sex with a colleague in his car.
Miss Purvor said: "We are trying to raise young children and we don't want to explain to them what is happening in these cars.
"I called the police because it is disgusting behaviour."
Another local, Colin Pearson, 34, said his suspicions were raised after spotting two hospital workers - one man wearing a tabard and a female nurse - spent an hour in a car on the road.
He said: "The car was rocking around a bit and it was obvious they were going at it like rabbits.
"They really need to wait until they get home, or if they are having an affair why not just do it in a hospital storeroom or something?"
Police confirmed that the neighbourhood police team was 'monitoring' the area after a number of calls from residents reporting lewd behaviour.
A spokesman for the hospital refused to comment on the dogging claims, but Susan Acott, the chief executive of Dartford and Gravesham NHS Trust, said: "I am sorry to hear about the difficulties caused by the cars in Powell Avenue.
"People who live in the vicinity or hospitals, schools and train stations are often troubled by cars parked outside of their houses at peak times."