The businesswoman, who took the Government to the Supreme Court over the EU Exit Bill and won, said her only aim was to ensure Article 50 was triggered in accordance with the legal requirements.
She said: “I’m delighted obviously that it’s been done along the legal requirements of Article 50 but I think we are far from saying the job is done.
“We have to ensure that for the next two years every action that the Government takes is along the legally required lines so if they try to bypass Parliament again there may be a need to step up again.
Gina Miller insisted she never wanted to stop Brexit after Article 50 was triggered today
“I never wanted to stop Brexit. My case was about ensuring that Article 50 was triggered along the lines of the legal requirement and that’s exactly what’s happened.”
Responding to Mrs May’s call for the country to come together to ensure Britain got the best deal, Ms Miller said: “Coming together means ensuring that it’s what’s best for Britain, it does not mean Mrs May and a few of her ministers’ idea of what Brexit is, it’s what’s best for the whole of Britain.”
The businesswoman also said she was puzzled by Mrs May’s Article 50 letter to Brussels.
“I’m puzzled by her letter because it’s actually quite a pro-EU letter,” Ms Miller said.
Theresa May signed the Article 50 letter on Tuesday
I never wanted to stop Brexit
“It’s like saying I love you, I believe in our relationship and our marriage by the way I’m going to go live with someone else. It was a rather strange tone.”
Mrs May signed the momentous letter in Downing Street just after 4.30pm on Tuesday.
Shortly before 12.30pm today, European Council president Donald Tusk confirmed he had received the notification of the UK’s withdrawal, posting on Twitter: "After nine months the UK has delivered. #Brexit"
In the letter, Mrs May outlined a number of negotiation principles including the sum of the EU exit bill, security and encouraging friendly negotiations.
The PM appeared keen to push back at the EU’s insistence the UK must agree its terms of exit – including a £50billion Brexit fee – before discussing a future trade relationship with the bloc.
Brexit day LIVE: images from around the country as Britain invokes Article 50 Wed, March 29, 2017
The country reacts as Theresa May officially invokes Article 50, and begins the process of Britain leaving the European Union
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Prime Minister Theresa May announces in the House of Commons that she has triggered Article 50, starting a two-year countdown to the UK leaving the EU
Mrs May wrote: “We believe it is necessary to agree the terms of our future partnership alongside those of our withdrawal from the EU.”
She did not, however, rule out paying some form of contribution upon the UK’s departure: "We will need to discuss how we determine a fair settlement of the UK's rights and obligations as a departing member state, in accordance with the law and in the spirit of the UK's continuing partnership with the EU.”]
Appearing to take a milder tone with the bloc after her Lancaster House speech earlier this year, where Mrs May said "no deal is better than a bad deal”, the PM told Mr Tusk: "The UK wants the EU to succeed and prosper."
Before signing off her letter, Mrs May also praised the European Union for "bringing together a continent blighted by war into a union of peaceful nations”.
She added: "Together, I know we are capable of reaching an agreement about the UK's rights and obligations as a departing member state, while establishing a deep and special partnership that contributes to the prosperity, security and global power of our continent".