She doesn't believe walking out of talks would help get a deal.
The British Prime Minister used a high-profile speech in London's Mansion House to dismiss the EU's insistence that it will not allow "cherry-picking" of rights and obligations, insisting that this was a part of any trade negotiation.
The agreement must respect the outcome of the referendum vote to "take control of our borders, laws and money".
In a speech Friday outlining her vision for future economic ties, May said: "U.K. and European Union regulatory standards will remain substantially similar in the future".
"The Prime Minister's commitment to agreeing a transition period by the end of March is vital because firms are making decisions on investment today".
A Cabinet source said: "There has been a fair amount of disagreement".
The EU is due to publish guidelines on Tuesday on how it sees the future relationship with the United Kingdom, although they are expected to be short and uncompromising, repeating the red-lines that the prime minister is attempting to rub out.
One of the most difficult Brexit questions is how to avoid a hard border between Britain's Northern Ireland and the Republic of Ireland. This is an agreement that we have all worked hard to protect. Her acknowledgment of the need for new labour mobility arrangements will also strike a positive chord with businesses.
The agreement must endure, without the need to return to the negotiating table "because things have broken down".
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"Fourth, it must be consistent with the kind of country we want to be as we leave: a modern, open, outward-looking, tolerant, European democracy; a nation of pioneers, innovators, explorers and creators; a country that celebrates our history and diversity, confident of our place in the world; that meets its obligations to our near neighbours and far off friends, and is proud to stand up for its values".
The Health Secretary dismissed suggestions the speech lacked detail but admitted it would be "very difficult" for the European Union to agree to the proposals put forward by the Prime Minister. We absolutely need to get this right if farming is to keep delivering for Britain's economy, environment and food security.
But she added: "Unlike some politicians, I have actually been straight with people because there are choices to be made".
The task will be to do that whilst moving to separate legal systems.
Contrasting his speech with British Prime Minister Theresa May's comments Friday on Brexit, Rutte said he wants to talk about "the best way to move forward with Europe".
Mrs May said: "The world is watching". If Brexit flops, he said, "there will be the most awful backlash". Mrs May has handed them a blueprint to achieve just that. They were asked to hand the copies back before leaving.
Mrs May said that in chemicals, aviation and medicine, Britain would seek to abide by European Union regulation, and she proposed a streamlined Customs partnership with the same tariffs at the border for goods sold to the EU.
Among her five Brexit tests was ensuring "our precious Union" emerged stronger through the process and she stressed it was her "duty" to represent all parts of the country.
"We will not be buffeted by the demands to talk tough or threaten a walk-out", she declared, noting: "Just as we will not accept the counsels of despair that this simply can not be done".
May acknowledged there will be limits, saying it is "time to face up to some hard facts". But we can't do it on our own, it is for all of us to work together.