The collective, made up of local lawyers, is suing the three firms along with 11 other defendants, claiming they are "unethical" and the licenses issued to the practices are illegal.
Also named in the petition are the Reserve Bank of India, which awards licenses, the Indian State and various Bar councils.
Anand Grover, counsel to the collective, said: "We do not want people to function in a totally illegal and unregulated manner.
"It's nothing to do with the fact that the people are foreign. Without enrolling on the rolls of the Bar Council they cannot practice the profession of law."
However, Ashursts senior partner Andrew Soundy said his firm was "hurt" by the action because it had followed the advice of local counsel who had not indicated a need to enrol.
"During 1994 it became apparent that clients wished us to become involved in their present and future activities in India, so we took local advice as to what we should be doing," said Soundy.
"We were advised by eminent lawyers in India that we should apply to the Reserve Bank for permission to open a representative office in Delhi.
He said permission was granted, subject to certain terms and conditions, and the firm was careful to operate within the terms of the licence.
"Now we find ourselves in the extraordinary situation where we've taken local advice, we've acted according to that advice and we were granted a licence, but we still face this action."
But Grover says the issue surrounding the granting of licenses is only one point on the agenda. The collective is more concerned with the unregulated practice of foreign law and the fact that lawyers from abroad are not sitting local Bar exams.
He said foreign lawyers were only allowed to act as conduits between their parent office and clients, but he alleged that the three practices were flouting the rules.
"I want them to comply with the law like we have to comply with the law in England.
"If the courts say that they can continue to practice law as they are, unregulated, then we will do the same."
Raj Pande, the attorney responsible for White & Case's Indian office, said the matter should be resolved through discussion rather than in a courtroom. But he said India had no framework to hold discussions between the government and foreign and domestic lawyers.