Young Britons from ethnic minority backgrounds risk being put off running for public office by the “nasty” divisive campaign run by Zac Goldsmith, the Tory candidate for mayor of London, his Labour rival told the Observer.

In an outspoken attack a month before Londoners choose a replacement for Boris Johnson, Sadiq Khan said he was worried Goldsmith’s tactics would deter young Muslims and others from playing a constructive part in society, and could damage the wider cause of integration.

Supporters of Khan, the Muslim son of a bus driver, say the Goldsmith camp has tried to focus voters’ minds on his faith, in an attempt to divide religious and ethnic groups and persuade non-Muslims to vote for Goldsmith.

They also say that Goldsmith’s campaign, run by Lynton Crosby, who masterminded the Tory success in last year’s general election, has tried to plant fear in Londoners’ minds by referring to Khan as a “radical” who has shared platforms with “extremists”. In comments defended by Goldsmith as legitimate, Michael Fallon, the defence secretary, said Khan was a “Labour lackey who speaks alongside extremists” and “cannot be trusted” to keep London safe.

Speaking to the Observer, Khan said: “It bounces off me – I’ve got thick skin – I learned to take abuse as an Asian kid growing up on a council estate in south London in the 1980s. But I worry about the impact on young ethnic minority kids – especially young Muslims.

“We need to be doing more to encourage young people from ethnic minority backgrounds to play a bigger role in society – whether being school governors, or standing for councils or for parliament.

“He’s clearly too weak to resist Crosby and co running a really nasty campaign. There is a real danger that Zac’s campaign will put the next generation off. It tells them it’s not worth sticking your head above the parapet, because look what’s happened to Sadiq Khan. That would be a real tragedy – bad for them, for integration and for society.”

A Goldsmith spokesperson said: “Zac’s campaigning hard across our city on his action plan for greater London … As the only candidate able to work with the government, he will always get the best deal for London.”

All parties are gearing up for elections on 5 May, which include the mayoral contest, the Scottish parliament and Welsh Assembly and local council elections across England.

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While Labour is downplaying its prospects in Scotland, Wales and English council elections, supporters of Jeremy Corbyn hope that a win for Khan will boost morale.

On Tuesday, Labour will launch its local election campaign in Harlow, Essex, with a message that the Tories have allowed spending cuts to hit the most deprived areas hardest. Jon Trickett, shadow minister for local government, will say that between 2011-12 and 2019-20, nine of the 10 most deprived councils in England will have seen cuts higher than the national average, with seven having cuts more than three times the national average. “It is an abuse of power that there can be a system in place where this happens,” Trickett said.

Dan Jarvis, MP for Barnsley Central, said: “Given that the Conservatives are in disarray and Labour has a reinvigorated membership … these elections are an excellent opportunity to significantly increase our political representation right across the country.”