A clear majority of the British public oppose Theresa May’s uncompromising Brexit negotiating position and are not prepared for the UK to crash out of the EU if the prime minister cannot negotiate a reasonable exit deal, according to a new poll.

In a sign that public support for the government’s push for a hard Brexit is increasingly precarious, just 35% of the public said they backed Britain leaving the EU without an agreement with other states. The UK would then fall back on to World Trade Organisation (WTO) tariffs, which MPs and business leaders have claimed would devastate the economy.

The survey – conducted by ICM for the online campaigning organisation Avaaz on the day the House of Commons voted overwhelmingly to trigger article 50 – suggests May would face a considerable backlash if Britain crashed out of the EU on WTO terms. In a welcome boost for soft Brexit campaigners, over half (54%) of those surveyed backed either extending negotiations if a satisfactory deal could not be reached, or halting the process altogether while the public was consulted for a second time.

The Liberal Democrat foreign affairs spokesman, Tom Brake, said the findings proved the government’s position was indefensible.

Of the 54% of people who opposed the government’s position, 34% said May should continue negotiating. A further 20% backed halting the process pending a second referendum on the terms of the deal, an option backed by the Lib Dems and a cross-party group of MPs including the Labour MPs David Lammy, Heidi Alexander and Ben Bradshaw, as well as the Green Party leader, Caroline Lucas.

Brake said: “Our best hope of stopping a ruinous hard Brexit that nobody voted for and few want is if the public rally round to fight it, as Brexit grows more unpopular. That means uniting many who voted leave but now want to avoid the economic catastrophe of quitting the single market, and who want to protect those European citizens who contribute so much to Britain’s economy and society.”

Bert Wander, Avaaz’s campaign director, said the results showed May was at odds with the public over Brexit, and called for the House of Lords to ensure that Britons had the right to force May to continue negotiating.

“Two-thirds of the public don’t want Theresa May dangling us over the Brexit cliff without a safety net and the Lords can intervene and save us from that fate. We need the right to send May back to Brussels if all she brings us is a bad deal for Britain.”