Battersea Dogs and Cats Home is calling on the Government to review the Dangerous Dogs Act 1991, because it says the current legislation is "flawed" and does not do enough to target irresponsible owners.
The law - which banned the pit bull terrier, Japanese Tosa, Dogo Argentino and Fila Braziliero breeds based on their physical appearance - was introduced 25 years ago this month.
By calling breed-specific offences in Section 1 of the Act "particularly controversial", the report states it results in the "unnecessary destruction" of healthy and good-natured animals with "little added protection to the public".
The charity quizzed 215 canine behaviour experts on factors most likely to cause a dog to attack and found that almost three-quarters of them said breed was at most only slightly relevant in influencing aggression levels in dogs.
A total of 86%, on the other hand, said the way a dog is brought up by its owner is an important attack factor - with the socialisation of man's best friend playing a critical role.
Claire Horton, Battersea's chief executive, said: "This new research by Battersea sets out the failings of the Dangerous Dogs Act 1991 in focusing on how a dog looks, rather than on anything that it has done or the actions of its owner.
"There are, of course, some dangerous dogs on our streets but for a quarter of a century this legislation has condemned too many innocent dogs to be put to sleep whilst systematically failing to reduce dog attacks in our communities.
"Battersea is dismayed that this outdated, knee-jerk piece of legislation is still on the statute books. There is a clear need to replace it with a law that targets irresponsible owners."
Last year the rehoming centre took in 91 pit bull terriers - which it said confirms that the breeding and sale of banned dogs is ongoing, and has simply been pushed underground.
The charity said 71% of these dogs could have been rehomed as family pets due to their friendly and affectionate nature, but under the law it was forced to put them down - including an 18-month-old named Francis.
Since 1991 there have been 30 fatal dog attacks - involving 16 children and 14 adults.
In response to Battersea's research, a Government spokeswoman said: "Dog attacks can have horrific consequences for victims and families, so the prohibition of certain types of dog under the Dangerous Dogs Act is crucial to help us deal with the heightened risk they pose.
"Any dog can become dangerous if it is kept by irresponsible owners in the wrong environment, which is why the Act covers any type of dog that is dangerously out of control."