The situation, which regularly causes loud noise like back-firing, has been going on for months at the large Shannon Corner store.
Tesco has already taken action including installing speed humps and changing parking restrictions outside of store opening times.
It says it will now take further steps to deter the anti-social behaviour, although it has not said what that action is.
A Tesco Spokesperson said: “We take reports of anti-social behaviour within our car parks extremely seriously and we continue to work proactively with the police to deter anti-social behaviour by groups of motorists in the car park of our New Malden Extra.”
