The groups want ministers to classify the clubs as "sex encounter establishments" rather than them just needing an alcohol license to operate.
One group warned, "Buying a lap dance is not the same as buying a cappuccino".
The movement has been joined by several councils and councilors, who have called for the licensing rules to be changed.
Currently, clubs outside London are treated in the same way as any ordinary bars or restaurants and only need an alcohol license to operate - making it difficult for residents to oppose them.
Campaigners say this is because of a loophole in the Licensing Act 2003, and that the number of clubs has doubled since 2004.
Classifying them as sex encounter establishments would give councils much greater say over where, when and how the clubs function.
It would also bring them into the same category as sex shops and sex cinemas - venues where nude entertainment is provided for the purpose of sexual stimulation.
Object and the Fawcett Society, groups which both campaign for women's rights, want new legislation to be introduced in the coming parliamentary session.
"Many local authorities have added their voice to growing calls for an end to licensing of lap dancing clubs as cafes," The Sun quoted Object's director Dr Sasha Rakoff, as saying.
"Current licensing has acted as a floodgate to the industry whilst making it difficult for local authorities and local people to have a say in this process.
"It has helped normalize lap dancing clubs and attitudes that encourage seeing women as sex objects, not people," Rakoff added.