In the first incident, a man in a balaclava with a baseball bat threatened and chased parking attendants before smashing their car in Brent Lea, Brentford.
During a second incident, an enforcement officer issuing a penalty charge notice (PCN) in London Road, Isleworth, was approached by six men, one of whom pushed the traffic warden.
Hounslow Council says the "disgraceful behaviour" from members of the public is "unacceptable" and it has the full support of local police, following the incidents in February.
Hounslow borough commander Raj Kohli said: “Parking attendants are part of the wider police family. But, much more importantly, they are human beings doing a job that has to be done.
“Their role is critical in making sure the roads of Hounslow are safe and clear for pedestrians and cars.
“I am actually dismayed that our colleagues have been abused in such a way and please rest assured that the Metropolitan Police will do its utmost in tracking down these offenders and ensuring that justice is delivered.”
In the Brent Lea controlled parking zone a man wearing a balaclava told two traffic wardens not to come back to the area.
When both men returned they were confronted again, and this time the man was armed with a baseball bat.
The officers fled the scene but were chased by the attacker who pushed a bike onto one of the men and continued to chase the other, who ran back to his car for safe cover, where the attacker violently smashed the car causing criminal damage.
In a separate incident, outside shops in London Road, a parking officer, from the new nighttime parking enforcement team, attempted to issue a penalty charge notice to a vehicle parked on double yellow lines.
While in the process of issuing the fine, the enforcement officer was approached by six men, one of whom became aggressive and pushed him. Police passing by spotted the incident and intervened.
Councillor Steve Curran, the leader of Hounslow Council, said: “This disgraceful behaviour is unacceptable.
“These officers were simply doing their job and tolerating violent and aggressive members of the public is not part of their remit.
“We have increased the number of parking enforcement officers and introduced our nighttime team at the request of residents who have complained about parking issues in their area.
“The solution is simple, don’t park where you’re not permitted to and you won’t be fined.
“We will always press for the strongest possible action where our staff are abused, confronted, threatened or, in the most extreme circumstances, injured.
“The people who react in this way towards our staff will find themselves left with more than just a parking ticket, they could be arrested and charged.
“We have the full backing of Hounslow Police who are supporting officers with joint patrols across the borough.”
One man is being questioned by police and another has been arrested in connection with the incidents.
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