Update - 2:30pm: Mrs May wrapped up her speech with a positive outlook for the future and said that the UK and EU neighbours would "stay linked by the many ties and values we have in common".
However, she acknowledged "there will be ups and downs over the months ahead" in the "rough and tumble" of the Brexit talks and that "no-one will get everything they want".
2:15pm: The Prime Minister brought up the border issue again in her speech, saying that the UK has already set out two options - a customs partnership or a "highly streamlined customs arrangement".
For the first option, at the border, the UK would mirror the EU's requirements for imports from the rest of the world, applying the same tariffs and the same rules of origin as the EU for those goods arriving in the UK and intended for the EU.
Under option two there would be "a range of measures to minimise frictions to trade, together with specific provisions for Northern Ireland".
There must be "no hard border" in Ireland after #Brexit, Theresa May says, saying UK will commit to keeping standards "as high" as the EU's and entering a "customs arrangement"https://t.co/bnayw3IWCU #RoadtoBrexit pic.twitter.com/jBb2IsJumz— BBC News (UK) (@BBCNews) March 2, 2018
2:05pm: Addressing a key concern on the movement of people, Mrs May said free movement will come to an end" as a result of Brexit but "UK citizens will still want to work and study in EU countries - just as EU citizens will want to do the same here".
On the EU criticism of the UK's "cherry-picking", she said: "What would be cherry-picking would be if we were to seek a deal where our rights and obligations were not held in balance. And I have been categorically clear that is not what we are going to do."
The Prime Minister said that the jurisdiction of the European Court of Justice in the UK would end and that she wanted to make sure the UK had a role in data protection arrangements.
2pm: Mrs May addressed the border issue early on her speech, acknowledging the particular challenges faced by Northern Ireland and Ireland.
The Prime Minister rejected the suggestion from some Brexiteers that the UK could unilaterally decide not to impose a hard border.
She said: "It is not good enough to say 'we won't introduce a hard border; if the EU forces Ireland to do it, that's down to them'.
"We chose to leave; we have a responsibility to help find a solution.
"But we can't do it on our own. It is for all of us to work together."
She went on the say that the UK wanted freedom to negotiate trade deals around the world, control of laws and "as frictionless a border as possible" with the EU.
The Prime Minister reassured that "no-one should be in any doubt about our commitment to the joint report we agreed in December" and said she hoped any issues with this withdrawal agreement would be resolved in the coming days.
1:45pm: In setting out her "vision for the future economic partnership" between the two, Mrs May began her speech by reiterating an early pledge to "make Britain a country that works not for a privileged few, but for every one of us" which will guide her negotiations.
Mrs May said that any deal reached must respect the result of the referendum, but stressed "tt was a vote to take control of our borders, laws and money", and "not a vote for a distant relationship with our neighbours".
10am: UK Prime Minister Theresa May is to deliver a keynote speech today on Brexit, just days after the EU published its draft Withdrawal Agreement, which Britain rejects.
Today's speech will focus on the future economic relationship between the UK and the EU, with Mrs May planning to tell EU leaders she wants the "deepest and broadest possible" trade agreement with the bloc as she seeks to lay the ground for the next phase of the Brexit negotiations.
In a keenly awaited keynote address due to begin at 1.30pm today, Mrs May will set out her vision of a free trade deal based on maintaining "high standards" of regulation, while managing any future divergence by the UK from existing EU rules.
While she will say that she wants Britain to have the freedom to strike trade deals around the world, it should be possible to agree a relationship with the EU where they continue to "support each other's interests".
At the same time she will stress that any agreement must respect the outcome of the 2016 referendum vote to take back control of "our borders, laws and money".
After her rejection on Wednesday of a draft EU proposal for Northern Ireland to remain in the single market and the customs union - unlike the rest of the UK - to avoid the return of hard border, she will say it must also preserve the UK's "union of nations".
Speaking at the Mansion House in the City of London Mrs May will set out "five tests" to guide Britain's approach to the continuing negotiations.
- The agreement must respect the outcome of the referendum vote to "take control of our borders, laws and money".
- The agreement must endure, without the need to return to the negotiating table "because things have broken down".
- It must protect jobs and security, with Britain and the EU continuing to pursue the "shared goals" of growing their economies while keeping their people safe.
- It must be consistent with Britain remaining "a modern, open, outward-looking, tolerant, European democracy" that stands by its international obligations.
- It must strengthen "our union of nations and our union of people".
Her speech comes after European Council president Donald Tusk warned that her insistence on taking Britain out of the single market and the customs union meant it could not enjoy "frictionless trade" with the EU after Brexit.
At talks in Downing Street on Thursday, where she briefed him on the address, Mr Tusk told her: "Friction is an inevitable side-effect of Brexit by nature."
- Press Association and Digital Desk