Barley, who is half British, sent her tweet after European Union lawmakers adopted a resolution on Wednesday that hinted at the possibility for Britain to reverse the Brexit process, stressing however that this would be possible only with the approval of all the remaining 27 member states.
A Downing Street spokesperson said that "The Prime Minister and President of the European Council Donald Tusk had talks this afternoon in Downing Street following last week's Article 50 notification".
"You will set the tone for Britain", the bloc's Brexit negotiator, Mr Michel Barnier, told Members of European Parliament (MEPs) just before the vote.
The Prime Minister was meeting Mr Tusk face-to-face for the first time since triggering Article 50.
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When Tusk replied two days later, he included a line implying Spain would be able to block the inclusion of Gibraltar in any future EU-UK trade deal, sparking a media and political dispute.
"They agreed to stay in regular contact throughout the Brexit process to keep a constructive approach and seek to lower tensions that may arise, also when talks on some issues like Gibraltar inevitably will become hard", the official said under condition of anonymity.
Downing Street said the Mrs May had made clear there could be no change to its status without the consent of its people.
Speaking to Donald Tusk, Theresa May said the United Kingdom would seek the "best possible deal" for Gibraltar in the Brexit talks.
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The dispute escalated as a former Tory leader, Lord Howard, suggested Britain could go to war to defend Gibraltar - just as the Thatcher government did in 1982 to recapture the Falkland Islands from Argentina. Asked if the talks had been successful he replied: "As always". But she has acknowledged that getting a final deal may take longer. We've said very clearly we want to maintain a deep and special partnership with the European Union and I think that has been reciprocated. We've got to deal with that now.
Earlier this week while on a visit to Jordan, Mrs May said she expected the shape of a new trade relationship to be clear to everybody by Brexit Day in March 2019.
'That's the sensible thing, it's the pragmatic way to look at this, and I believe that's what we will do'.
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She announced her opposition in a statement posted to Medium , faulting the nominee for "a stunning lack of humanity". But at least Democratic senators will be able to tell their constituents that they are Resisting.