Sadiq Khan, the newly elected mayor of London, called on Labour on Sunday to "stop talking about ourselves" and broaden its appeal in the latest criticism of the opposition party's hard-left national leader, Jeremy Corbyn.

Khan, 45, was elected the first Muslim mayor of London last week, defeating a challenger from the ruling Conservatives who had attempted to link him to extremism in a campaign also marred by charges of anti-Semitism.

The former human rights lawyer denounced the campaign against him in an interview on the BBC, calling it "nasty" and "divisive". But he reserved more criticism for his own party, which struggled in local elections on Thursday.

He said Labour could win the next parliamentary election only if it started talking to those people who have left its ranks or were voting for the Conservative Party and smaller parties such as UKIP.

"My point is this – I want a big tent," he told the Andrew Marr show. "We've got to speak to everyone, there is no point us just speaking to Labour voters, our core vote."

It was a clear criticism of Corbyn, a socialist who was elected leader of Labour last year on a wave of enthusiasm, among mostly younger members, for change and an end to 'establishment politics'.

Despite enjoying some of the highest levels of membership in the party, Corbyn has been criticised by several Labour MPs for concentrating on issues precious to him, but which have only marginal interest for the public, such as Britain's nuclear deterrent.

Corbyn opposes the renewal and maintenance of the Trident nuclear submarine programme.

In a newspaper article, Khan urged Labour to follow in his campaigning footsteps if it wanted to win at a parliamentary election in 2020.

Khan, the son of a bus driver, won with a convincing lead of more than 13 per cent over Zac Goldsmith, the son of a billionaire financier, despite the bitter campaign, which Conservative leaders defended as the "rough and tumble" of politics.

Khan condemned the Conservatives' tactics and said Labour should also learn from the divisive campaigning, and move more quickly and forcefully to tackle charges of anti-Semitism in the party's ranks.

"How can you expect to enthuse an undecided voter, or persuade a previous Tory voter, if you can't gain their trust on the key issues, or you don't want to talk about what they care about most?" Khan wrote.