Theresa May has told the European Council President Donald Tusk that Gibraltar’s sovereignty is not up for negotiation in her first face-to-face talks with the European Council President since she triggered Article 50.

Mrs May welcomed Mr Tusk to Downing Street for lunch eight days after giving him formal notice of Britain’s intention to leave the EU.

Downing Street sources said they had “a general, broad chat”, but the two leaders are understood to have agreed on the need for an early deal on migrants’ rights to give EU citizens in the UK and Britons living in the EU certainty about their future.

Officials said the meeting was “very constructive”. One insider said: “They both said ‘let’s get this done’.”