London (CNN) At the eleventh hour, Theresa May claims to have made a breakthrough in Brexit negotiations.

During talks with the European Union in Strasbourg late Monday, the UK Prime Minister and Brexit Secretary Stephen Barclay "secured legally binding changes" to "strengthen and improve" the UK's agreement on withdrawing from Europe, Cabinet Office Minister David Lidington told Parliament in a statement.

Those changes would not affect the terms of the withdrawal, but offer legal assurances to back it up.

European Commission President Jean-Claude Juncker tweeted that the changes provide "meaningful clarifications and legal guarantees."

"The choice is clear," he said. "It is this deal, or #Brexit may not happen at all. Let's bring the UK's withdrawal to an orderly end. We owe it to history."

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