A 42% increase in incidents involving dangerous dogs in the last year is concerning enforcement officials.
The RSPCA and Wandsworth Council are voicing worries some owners are too young to be in control of powerful dogs and have them as status symbols.
Others can use them for intimidation in connection with robbery, say police.
The council says it wants dog licences introduced with age limits and the RSPCA is also calling for very young people not to own large dogs.
"Without proper control they can quickly become a danger," said RSPCA Inspector Jan Eachus.
He added a lack of control was not good for the animal either.
Dog owner Mike Ebberson explained he and his dog were attacked by two large dogs when they were out on a recent walk.
He was badly injured, his dog had to be put down and an armed police response unit was called, leading to the shooting of one of the attacking dogs.
A youth has been charged in connection with the incident.
Police figures show there were 719 incidents involving dangerous dogs in 2005; 797 in 2006; and 306 in the first four months of 2007 - compared with 215 in the first four months of last year.