By William James and Kylie MacLellan

LONDON (Reuters) - Britain will give up its planned presidency of the European Council, due to start in July 2017, to focus on negotiating the country's exit from the European Union a spokeswoman for Prime Minister Theresa May said on Wednesday.

The decision, reached in a phone call between May and EU Council President Donald Tusk on Tuesday evening, reflects the scale of the task facing Britain as it seeks to negotiate a new relationship with the EU after a June 23 public vote to leave.

"The Prime Minister suggested that the UK should relinquish the rotating Presidency of the Council, currently scheduled for the second half of 2017, noting that we would be prioritizing the negotiations to leave the European Union," the spokeswoman said.

"The Prime Minister explained that we will need to carefully prepare for the negotiations to leave the EU before triggering Article 50," she said, referring to the formal legal process for leaving the bloc.

"Donald Tusk reassured the Prime Minister that he will help to make this process happen as smoothly as possible."

A spokesman for Tusk said there had been no decision yet on who would take up the vacant slot, and that discussions on the issue would begin immediately between ambassadors.

The presidency is currently held by Slovakia and is due to be handed over to Malta for the first half of 2017. Estonia was due to follow the British presidency.

Possible solutions could be to extend Malta and Estonia's terms by three months to cover the gap or for Belgium to step in for the six months.

(Additional reporting by Philip Blenkinsop in Brussels, editing by Guy Faulconbridge)