The investment fund manager, who brought the case against the Government, blasted Mrs May for expecting to be “unanswerable or unchallenged”.
Ms Miller has been accused of trying to derail Brexit, but insisted her legal challenge was made to uphold and protect Parliament “sovereignty”.
Speaking outside the Supreme Court in London after eight of the 11 judges ruled in her favour, she said: “Only Parliament can grant rights to the British people and only Parliament can take them away.
Gina Miller said "no prime minister was unanswerable"
No prime minister, no Government can expect to be unanswerable or unchallenged
“No prime minister, no Government can expect to be unanswerable or unchallenged – Parliament alone is sovereign.
She claimed the ruling allowed MPs the “rightful opportunity” to bring their “invaluable experience and expertise” to help the Government select the “best course” for the forthcoming Brexit negotiations.
“There's no doubt that Brexit is the most divisive issue of a generation but this case was about the legal process and not politics," she said.
Gina Miller insisted she was not trying to derail Brexit
Ms Miller told the press, the case ensured Britain’s democratic process and would now allow the Government to trigger Article 50 “legally”.
During the statement, she alluded to “the levels of personal abuse” she had received over the last seven months for simply asking a “legitimate question”.
“I sincerely hope that going forward people who stand in positions of power and profile are much quicker in condemning those who cross the line of common decency and mutual respect,” she continued.
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“Lastly, I would like to whole-heartedly thank those who have sent me the most heartwarming messages of support. They have truly helped bolster me in this most arduous process – thank you.”
Who is Gina Miller?
Thu, November 3, 2016
Gina Miller is leading the challenge that has blocked Theresa May triggering Article 50 without the consent of Parliament, take a look back at Miller's background.
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Gina Miller has won the case to block Theresa May from Article 50
Ms Miller’s victory means the prime minister now has just 67 days to secure the consent of both MPs and unelected Lords before she can begin EU divorce talks.
The Conservative leader has promised to trigger Article 50 by the end of March, previously insisting “royal prerogative” powers gave her the right to do so without a vote by Parliament.
Although losing the legal case is significant, the Government vowed it’s Brexit timetable was still on track.
A Number 10 spokesman said: “The British people voted to leave the EU, and the government will deliver on their verdict – triggering Article 50 as planned – by the end of March. Today's ruling does nothing to change that."
Supreme Court judges upheld a High Court ruling meaning Parliament will vote on Article 50
Brexit Secretary David Davis will make a statement on Tuesday afternoon setting out details of the Government's legislative response in the House of Commons.
It’s believed draft legislation has already been prepared in preparation for the appeal being rejected.
It’s rumoured the bill will be short and aimed at authorising Brexit negotiations, which MPs could not vote on as early as next week.