The Isle of Wight's Wildheart Trust has handed been to London to hand in a petition, calling on the government to ban the cross-breeding of exotic cats with domestic cats.
The Sandown charity's representatives met with MPs and Lords, handing in the names of more 15,000 people who agree it should be stopped.
Hybrid cats fetch up to £20,000 per kitten and welfare standards can be low.
The Wildheart Trust rescued two in France (called Xirus and Tafkap, now living more happily in Yaverland), who had broken and deformed bones. They were destined to bred with domestics, to produce the Savannah cat.
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The hybrid animals do not make good pets because they spray urine and can be aggressive and find separation difficult, according to the Trust.
Hybrid cats are also a bigger threat to UK native species than normal domesciated cats but, unlike other non-native animals, they are not regulated by UK legislation.
Lawrence Bates, Chief Operating Officer of the Wildheart Animal Sanctuary, said: "A practice such as this has no place in a forward thinking nation of animal lovers.
"Every MP and Lord we met during our recent trip to London was shocked to discover it is still legal in the UK and all have pledged to support an amendment to ban it.
"It is incomprehensible to think that the law allows people to manufacture new types of animal, creating powerful predators that pose a significant threat to our native species”
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