Battersea Dogs and Cats Home is calling on the Government to review the Dangerous Dogs Act 1991, saying current legislation is "flawed" and instead should 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.
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".
Findings from a survey of 215 canine behaviour experts, who were quizzed by the charity on the factors most likely to cause a dog to attack, have been released to coincide with the anniversary.
The What's Breed Got To Do With It? report reveals 74% of professionals said breed was either irrelevant or only slightly important in determining aggression levels in dogs.
A total of 86% 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.
A dog's size was only considered relevant in terms of an attack outcome as "small dogs are just as likely to attack as larger dogs", but larger dogs have the capacity to "inflict greater injury and damage".
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"Battersea is dismayed that this outdated, knee-jerk piece of legislation is still on the statute books.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 re-homing centre took in 91 pit bull terriers - which they say confirms the breeding and sale of banned dogs is ongoing, and has simply been pushed underground.
The charity said it believes 71% of these dogs could have been rehomed as family pets due to their friendly and affectionate nature - but under the law were forced to put them down.
Battersea has also released pictures of 25 of the pit bull terriers it had to put to sleep purely for their looks alone - with 18-month-old Francis set to become latest victim of the act.
Since 1991 there have been 30 dog-attack fatalities - involving 16 children and 14 adults.
Calling breed-specific legislation "flawed", the report highlights how the four types of dogs outlawed as dangerous under the act were not directly identified as the most frequently-aggressive by experts.
Trevor Cooper, Battersea's legal consultant and dog law solicitor, said the "law must be repealed" because "assuming a dog is dangerous because of the way it looks just doesn't stand up to scrutiny".
The act also makes it a criminal offence to allow a dog to be dangerously out of control in a public place, or in a non-public place where the dog is not permitted to be.
Since its introduction there have been amendments to the legislation - in 1997 the mandatory destruction of banned breeds was removed and the Index of Exempted Dogs reinstated.
Decided by the courts, if they perceive an owner to be a responsible person and the banned dog presents no danger to public safety, the animal will be added to the index but must be kept by the owner under strict conditions such as being muzzled and on a lead in public.
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."