British Prime Minister Keir Starmer, reeling from a crushing local election defeat, faced a new setback to his leadership when an Australian-born former minister said she would challenge him for the top job if no one else stepped forward.Starmer's Labour Party recorded the worst losses of a governing party in municipal polls since 1995, prompting a growing number of his own lawmakers to call on him to quit.To try to shore up his position in the party earlier on Saturday local time, he named two influential Labour grandees as advisers, former prime minister Gordon Brown and former deputy Labour leader Harriet Harman.But just hours later, Labour politician Catherine West, a former minister, told BBC Radio that she wanted the cabinet to work out a plan to replace Starmer by Monday, or she would challenge him for the position herself."If .. Asked whether he would stand down, he told British media that it was not the right thing to do."I'm not going to walk away from this," he said earlier on Saturday.Several Cabinet ministers said on Friday that they continued to support Starmer, who just under two years ago led Labour to a landslide national election victory, and an immediate challenge from the potential leadership rivals does not look straightforward.Greater Manchester mayor Andy Burnham does not have the seat in parliament he needs to mount a challenge, and former deputy prime minister Angela Rayner has yet to fully resolve the tax issues that prompted her resignation from office last year.Wes Streeting, currently health minister, is, like Starmer, tainted by the appointment of Peter Mandelson as Britain's ambassador to the United States