In a speech aimed at answering critics who have accused the UK Government of failing to grasp the tough realities of leaving the EU, Ms May said Britain wanted "the broadest and deepest possible agreement - covering more sectors and cooperating more fully than any free trade agreement anywhere in the world today".
Mrs May's speech will insist that, throughout the Brexit negotiations, she will be guided by her promise made on the doorstep of Downing Street when she first took her job in July 2016 to "forge a bold new positive role for ourselves in the world and make Britain a country that works not for a privileged few, but for every one of us".
She will call for "a bold and comprehensive economic partnership with our neighbours in the European Union, and reaching out beyond to foster trade agreements with nations across the globe".
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.
"This is a negotiation, and neither of us can have exactly what we want", she said.
"As we think about how we set up a new partnership with Europe, there are very entrenched positions on both sides", he said.
One of the most difficult Brexit questions is how to avoid a hard border between Britain's Northern Ireland and the Republic of Ireland.
Boris Johnson, the Foreign Secretary, who was prevented from attending the speech because of the snow, tweeted a picture of himself giving a thumbs-up while arch-Brexiteer Jacob Rees-Mogg praised the PM for her "statesmanlike speech", which he said had set out the hard facts about leaving the EU. We understand your principles.
"It is possible to have that frictionless trade that we all want, that prosperous economy, at the same time as getting back control of our destiny", he said.
The task will be to do that whilst moving to separate legal systems.
But at a meeting of the European parliament's Brexit steering group on Wednesday evening, led by the former Belgian prime minister Guy Verhofstadt, MEPs concluded that the United Kingdom had not gone far enough.
Huw Jones says Scotland must improve further to beat Ireland
Jones was impressed by the home performance and blamed himself for only the second defeat of his 26 Tests in charge. If there was, we shouldn't let that detract from a great Scotland victory. "Don't get distracted by other things".
Mrs May was said to have agreed to a series of changes to the text requested by ministers.
She said a customs partnership could keep the same border tariffs for goods intended for the European Union but different ones for those going into the UK.
"Most of the points raised were about nuances of language", the source said.
But although May did not dispel the impression of "cherry-picking" European Union benefits or of trying to have Britain's cake and eat it, European Union officials working on the negotiations behind the scenes welcomed what one called her "positive directional language".
In her speech, Mrs May warned that "no-one will get everything they want" out of Brexit negotiations but she is confident a deal can be done.
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.
May is making a speech outlining her vision of future economic ties with the EU.
May acknowledged there will be limits, saying it is "time to face up to some hard facts".
"It is one small part of a jigsaw that is gradually being put together and we don't know what the whole picture will look like in the end, but businesses and people will adapt to it".
The Prime Minister used a high-profile speech to call for "pragmatic common sense" to deliver a Brexit deal that will be good for Britain and Europe, as she sent a message to Brussels: "Let's get on with it".