Theresa May faces an uphill task to get parliament to back her EU divorce plan

Britain faces "more division and more uncertainty" if a draft Brexit deal falls through, Prime Minister Theresa May said on Friday as she sought to win over sceptical Britons ahead of an EU summit this weekend.

In a call-in show on BBC radio, May also refused to say whether or not she would resign if the British parliament eventually voted down the divorce agreement and outline on future ties.

"This isn't about me... I am focused on ensuring we get this deal," she said, adding that she would be touring Britain to explain the agreement "to people up and down the country".

"If this deal does not go through we are back at square one. What we end up with is more division and more uncertainty," she said.

May, who voted to stay in the European Union in the 2016 referendum, also dismissed calls for a second vote with an option to keep Britain in the EU, but then refused to say whether her deal was preferable to remaining in the bloc.

Instead, she said Britain could build a "better future" for itself outside the European Union.

She repeated her position on British sovereignty over Gibraltar -- a contentious issue with Spain that in recent days has threatened to upend the EU summit on Sunday.

"We're very clear, as the UK, that when we negotiate on these matters... we do so on behalf of the whole UK family including Gibraltar," she said.

May's spokeswoman told reporters earlier on Friday: "We've negotiated very openly and constructively with the EU in matters relating to Gibraltar and worked closely with Spain.

"The withdrawal agreement isn't being re-opened. We will work with the government of Gibraltar and Spain on our future relationship," she said.

May is due to travel to Brussels on Saturday for last-minute talks with European Commission President Jean-Claude Juncker ahead of the summit.