Prime Minister Keir Starmer pledged Monday to prove the “doubters” in his own party and among the electorate as a whole wrong as he tries to fight off demands to step down after devastating local election results for his Labour Party . Starmer argued that he will “face up to the big challenges” and restore hope to the country. That includes getting closer to the European Union and “putting Britain at the heart of Europe,” a decade after the U.K. voted to leave the EU. “I know I have my doubters and I know I need to prove them wrong, and I will," Starmer said during a speech in London . He vowed to prove to millions of people “tired of a status quo that has failed them” that the government is on their side. He said Labour is in “a battle for the soul of our nation,” and the U.K. will go down “a dark path” if Reform UK, the anti-immigration party led by Nigel Farage, comes to power.…