The two-partner firm, which specialises in mental health and community care law, claims Lord Irvine's plan to allow only law firms with contracts to practice legal aid work is illegal.
Yesterday, in a case backed by the Law Society, Mr Justice Latham gave the green light for the issue to be judicially reviewed.
The contracting restrictions - set to come into force next month - contravenes the Legal Aid Act 1988 which permits clients to use the solicitor of their choice, says Mackintosh Duncan.
Earlier this month, the Lord Chancellor's Department announced that the number of firms allowed to offer civil legal aid is to be cut by more than half to just 5000.
Mackintosh Duncan, which has not been given an assurance that it will win a contract to provide legal aid work for mental health and community care, claims contracting will deny vulnerable people access to justice.
Law Society president, Bob Sayer says: "The Mackintosh Duncan case raises vital questions about whether help from the legal aid scheme will be available for vulnerable clients."