The mayor of London has issued a dramatic call for another referendum on EU membership, insisting that the people must be given the chance to reject a Brexit deal that will be bad for the economy, jobs and the NHS.

Writing in the Observer, Sadiq Khan says that, with so little time left to negotiate, there are now only two possible outcomes: a bad deal for the UK or “no deal” at all, which will be even worse. “They are both incredibly risky and I don’t believe Theresa May has the mandate to gamble so flagrantly with the British economy and people’s livelihoods,” he writes.

Khan says that backing a second referendum was never something he expected to have to do. But so abject has been the government’s performance, and so great is the threat to living standards and jobs, he says, that he sees no alternative than to give people a chance to stay in the EU.

“This means a public vote on any Brexit deal obtained by the government, or a vote on a ‘no-deal’ Brexit if one is not secured, alongside the option of staying in the EU,” he writes. “People didn’t vote to leave the EU to make themselves poorer, to watch their businesses suffer, to have NHS wards understaffed, to see the police preparing for civil unrest or for our national security to be put at risk if our cooperation with the EU in the fight against terrorism is weakened.”

Theresa May is travelling to Austria as part of efforts to secure a Brexit deal with EU leaders. Photograph: Toby Melville/Reuters

The intervention from one of Labour’s most powerful politicians will put yet more pressure on the party leader Jeremy Corbyn to throw his support behind another referendum at Labour’s annual conference, which opens in Liverpool next weekend.

More than 100 anti-Brexit motions, and motions backing another referendum, or people’s vote, have been submitted by constituency parties – believed to be a record for any single issue in the party’s recent history.

A large number of the motions are from the left of the party, and call for a commitment to a people’s vote to be inserted into Labour’s next general election manifesto.

Sam Tarry, national political officer of the TSSA union, who used to work for Corbyn, said the left of the Labour party was uniting behind demands for another vote: “The sheer weight of anti-Brexit motions going to conference is unlike anything I have ever seen – and the only force in the Labour party capable of pulling that off is the left. The trade union movement has moved quickly towards an anti-Tory Brexit position this summer. There is this feeling that we, the socialist left, simply cannot stand by and watch while workers and communities are sacrificed at the altar of Tory dogma and imperial nostalgia.”

Until now Corbyn and the shadow chancellor, John McDonnell, have said they would prefer the public to be given a say on Brexit in a fresh general election, adding that, if one does not happen soon, the option of a second referendum should remain open. But leftwingers in the party now say this formula is not sufficient, and want a commitment to another referendum in the next manifesto.

Alena Ivanova, a leading activist for the grassroots group Momentum in east London, said: “This is a campaign now being led by the left... Tory Brexit is a fundamental threat to the rights and prosperity of working-class people and the communities that Labour represents, driven by bosses and rightwing ideologues. We will only stop it with unashamed leftwing internationalism and, crucially, that will also help us in the campaign to get the Corbyn government we need.”

Recognition of the case for a new referendum also appears to be growing in Tory circles. On Saturday the Conservative MP George Freeman, a former chair of Theresa May’s policy board, said on Twitter that pressure for a second vote would become “overwhelming” should moderate Conservatives fail to shape a sensible Brexit deal.

Last week the Bank of England governor, Mark Carney, warned the cabinet that the impact of a no-deal Brexit could be as catastrophic as the financial crisis that crippled the economy a decade ago. He also said that house prices could fall by 35% over three years in the worst-case scenario.