LONDON (Reuters) - British opposition Labour Party leader Jeremy Corbyn said on Thursday the result of last month's vote to leave the European Union should be respected, putting him at odds with the lawmaker who is challenging him for his job.

Labour has been locked in a bitter power struggle since the June 23 vote to leave the EU, with critics of Corbyn saying he did not work hard enough to persuade the party's voters to back remaining in the bloc.

Owen Smith, who has said Britons should get to vote again on leaving the EU once a Brexit deal is decided, is running against Corbyn in a leadership contest triggered by Labour lawmakers who say they had lost confidence in his ability to lead the party and win an election.

"I think you have to respect the result of the referendum whether you welcome it or not," Corbyn told BBC Newsnight.

Corbyn, who launched his leadership campaign earlier on Thursday, also said securing access to European markets would be a key party of any Brexit deal, but he also wanted to see some freedom of movement retained.

Immigration was a key part of the debate ahead of last month's vote and new Prime Minister Theresa May said on Thursday that she was clear the government should and would deliver on the British people's wish for control on free movement.

"I would want to see a movement of labor which recognizes the need to have similarity of conditions across Europe," said Corbyn.

"If we say we are going to start restricting then it works both ways, it will also restrict British people going to live and work in Europe. I think that is going to be impossible within the single market."

(Reporting by Kylie MacLellan)