LONDON, May 21 (Reuters) - Britain is prepared to walk away from divorce talks with the European Union without a deal, Brexit minister David Davis said on Sunday, but stressed that he thought an agreement was the most likely outcome.

Talks will begin next month on untangling Britain's relationship with the EU and forging a new trade deal after Britons voted last year to leave the 28-country bloc.

Wary of some in the bloc who might want to see Britain punished for leaving, Prime Minister Theresa May has said that unless she gets the kind of deal she wants from Brussels, she will withdraw without any accord.

The threat has been criticised by her political rivals ahead of a June 8 domestic election as creating unnecessary uncertainty for businesses and setting a potentially damaging tone for the talks.

Davis said the threat was genuine and that Britain was prepared to see it through.

"We don't need to just look like we can walk away, we need to be able to walk away," he told the Sunday Times newspaper. "Under the circumstances, if that was necessary, we would be in a position to do it."

In a separate interview, May told the Telegraph that she wanted past contributions to the bloc to be taken into account when working out one of the thorniest issues of the divorce: how much Britain should pay to Brussels when it leaves.

"There is much debate about what the UK's obligations might be, or indeed what our rights might be in terms of money being paid in the past. We would look at those, both rights and obligations," she said. Chief EU negotiator Michel Barnier told his Commission bosses the EU would focus on securing citizens' rights, financial issues and borders, and that he hoped for a deal on these issues between October and December.

If that timetable holds, the EU would be ready to start discussing the shape of its future trade relationship with Britain and a transition period leading to it between December 2017 and spring 2018.

"There are plenty of people in the European Union who want this to succeed. There may be some who want it to fail," Davis said. "I'm of the view that the likeliest outcome is the outcome we are looking for." (Reporting by William James; editing by Richard Lough)