Sadiq Khan, the mayor of London, will warn on Wednesday that the Brexit plan outlined in Theresa May’s speech on Tuesday could “rip Britain apart”, striking a markedly different tone to the Labour frontbench.

Khan, a former Tooting MP, will tell an audience at the World Economic Forum in Davos that “hard Brexit would be a lose-lose situation”. On May’s speech, he says: “A hardline approach to Brexit may hold the Conservative party together, but it could rip Britain apart.

“And if we continue on this path – towards a hard Brexit – we risk having to explain to future generations why we knowingly put their economy, their prosperity and their place on the world stage in such peril.”

He will say that privileged access to the single market is “critical for London” – that nothing else will do.

Khan’s tough approach comes amid growing disquiet among Labour MPs, including some frontbenchers, about whether Jeremy Corbyn, and the shadow Brexit secretary, Keir Starmer, were too generous to the prime minister after her Brexit speech.

May’s “plan for Britain”, involves leaving the EU single market, and dropping key aspects of the customs union – but seeking a wide-ranging trade deal with the rest of the EU.

Corbyn offered strong resistance to May’s threat to turn Britain into what he characterised as a “bargain basement” on the shores of Europe, but both he and Starmer welcomed her decision to seek “access” to the single market, instead of trying to retain membership.

Khan is sometimes touted as a potential future Labour leader, and his party conference speech in September, with its repeated references to “Labour in power”, was widely regarded as a dig at Corbyn and his low poll ratings.

Labour is in an awkward position, seeking to square the circle between its pro-remain members and voters, and the profound concerns of some of its traditional supporters in former industrial areas about immigration.

Moderate MPs, including former shadow chancellor Chris Leslie and Progress chair Alison McGovern, have warned that their party must offer what McGovern, in an article for Labour List, called, “real opposition to what May announced yesterday”.