May urged “creativity” in her Florence speech and Brussels welcomed some of her comments.
She made two concessions to what some see as Brexit reality: that the future relationship with the EU will have to be finalised after the UK leaves the EU, and that the UK must pay for what it committed to over the 2014-2020 period.
Several issues still need to be resolved, including citizen rights, before the EU says the talks can proceed to the next phase.
The speech, on Friday, attracted a range of differing opinions.
Parliament's ECR group co-Chair Syed Kamall said he thought the Prime Minister had "taken a decisive step" towards shaping a final deal for the UK leaving the EU by clarifying Britain's position.
He added, "We can only hope that the EU takes what the Prime Minister has said seriously, and sees that it is time to move forward. I hope that the clarity provided today will allow for real progress at the next round of negotiations.
"Clarifying the rights of EU citizens in the UK and UK citizens in EU countries, the future UK-EU trading relationship and settling outstanding financial commitments are the biggest issues on the table, and the Prime Minister has been clear what she wants from these negotiations, and how far she is willing to go.
"EU leaders need to realise that the British people voted to leave the EU in order for things to be different. Our future relationship should be less about open cheques and more about open trade.
"We need to start talking about our future trading relationship. The UK and EU’s future trade relationship is just as important for EU jobs and business, as it is for those UK companies that trade with EU companies and customers.
"Of course there are two sides negotiating to get the best possible deal for those they represent; but I hope that at the end we can all come together and shake hands believing everyone played fair, so that we can all move towards with a close and productive future relationship built on trade and cooperation where we continue to have mutual interests.
Kamall's group colleague Ashley Fox, who leads Parliament's delegation of Conservative MEPs, urged the EU to respond positively to May's landmark speech in Florence.
He said, "Brussels has been asking for concrete proposals and here they are.
"Theresa May's plan for a time limited transitional period, during which our budget contributions would continue, provides certainty for business, stability for the economy and addresses the concerns of our European partners. The speech also contains a promise that the UK will honour its financial commitments and important new legal guarantees for EU citizens in the UK and British citizens in the EU.
"The Prime Minister has laid out the basis of a new and fruitful relationship between Britain and the EU and I hope the EU now responds by agreeing to move onto the next substantive phase of negotiations.
"I trust European leaders will accept the invitation to mould a unique new relationship with Britain that secures long term prosperity and security for us all.”
Fox added, "It is time we got down to business and Conservative MEPs will be conveying that message very strongly in Brussels.
"The Prime Minister has delivered a blueprint for our country's future. I hope Florence proves to be the cradle of a renaissance for both Britain and the EU."
German Greens MEP Sven Giegold told this website,"May has taken the first step of facing reality. May's proposal for the transition period is a step in the right direction, but must not divert attention from the financial obligations that the UK has already made. A transition period comes with equal rights and equal obligations."
He added, "There can be no special treatment for access to the internal market for Great Britain. May has to tell her citizens the plain truth. That means that her proposal must include the outstanding payments to Europe and should not give the impression that there is access to the internal market at special conditions."
Giegold said, "That includes, paying the contributions to the EU budget, applying and enforcing all rules as well as the four fundamental freedoms including freedom of movement. This is the kind of truth and honesty British citizens never received from Brexiteers."