Britain's Prime Minister, Theresa May, delivers a speech to launch the Conservative Party's local elections campaign, in Calverton Village Hall, Calverton, Britain April 6, 2017. REUTERS/Andrew Yates

LONDON/BRUSSELS (Reuters) - British Prime Minister Theresa May and European Council President Donald Tusk agreed on Thursday to try to lower tensions in upcoming Brexit talks, especially over issues like Gibraltar.

The future of the rocky British enclave on the southern tip of Spain became the first big point of controversy in Brexit negotiations after the EU draft position said the application of any EU-UK trade deal to Gibraltar had be agreed between Spain and Britain.

Meeting Tusk for the first time since she began the divorce process on March 29, May said Britain was looking forward to formally beginning talks with the European Union once the bloc has agreed its guidelines.

“The PM also made clear that on the subject of Gibraltar, the UK’s position had not changed: the UK would seek the best possible deal for Gibraltar as the UK exits the EU and there would be no negotiation on the sovereignty of Gibraltar without the consent of its people,” May’s office said in a statement.

Gibraltar rejected the idea of Britain sharing sovereignty with Spain by 99 percent to 1 percent in a 2002 referendum, but voted overwhelmingly to remain part of the EU in last June’s referendum on EU membership.

An EU official said Tusk and May had a “good and friendly” meeting lasting nearly two hours at the British leader’s Downing Street official residence,

“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 difficult,” the official said under condition of anonymity.