"Whilst prorogation is an acceptable UK constitutional practice, no prime minister in modern history has attempted to use it in such a brazen manner," Ms Miller wrote on a fundraising website set up fund the urgent application to the high court for a judicial review.
Ms Miller, who rose to prominence when she won a legal case forcing parliament to legislate before article 50 could be invoked, said the decision to suspend parliament a few weeks before the Brexit deadline was a "dark day for democracy".
Opponents say it stop MPs from playing a full part in the Brexit process as the time they will have to pass laws to stop the UK leaving without a deal on 31 October would be cut.
Mr Johnson meanwhile said a Queen's Speech would take place after the suspension, on 14 October, to outline his "very exciting agenda".
Launching her legal campaign Ms Miller said that "all Britons, who believe in the rule of law and the preservation of Britain’s internationally respected and democratic traditions, will share my profound sense of dismay at this cynical and cowardly action."
She added: "The desperation of using prorogation in this manner illustrates just how unscrupulous the Prime Minister and his advisers have become. They would even cause a constitutional outrage to force through their ideological agenda. They know they lack the legitimate and moral authority to involve our elected representatives and are therefore seeking to bypass them.
"These actions are more akin to dictatorship than democracy and as such their legality must be tested in the courts. But we cannot do it alone. Your help, support and generosity will mean we have the resources to act as swiftly and effectively as possible in the extremely limited time we have available."
As a result, she said she had instructed her legal team "to once again defend our parliament’s sovereignty by launching an urgent application for Judicial Review."
Her announcement came after a motion was filed at the Court of Session in Edinburgh by a cross-party group of more than 70 MPs and peers in a bid to stall Mr Johnson.
Lawyers acting for the Scottish National Party’s Joanna Cherry and 74 other MPs and peers expect to be in court in Edinburgh later this week to block the suspension of parliament.
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