Senior Tory and Labour MPs called on Theresa May to forge a new cross-party approach to Brexit as fears grew that the prime minister’s weakness could lead to the imminent collapse of talks on the UK’s exit from the European Union.

In a dramatic demonstration of May’s loss of authority, as a result of Thursday’s general election – which stripped her of a Commons majority – the MPs demanded that she in effect drop her own Tory “hard Brexit” plans in favour of a new “national” consensus, that would be endorsed by members from all sides of the House of Commons.

The proposal, if adopted, would throw open the debate on what kind of Brexit the country wants, with just a week to go before May is due to lead the country in formal negotiations with the EU on the terms of exit.

It comes as senior EU figures expressed their concerns that the process could collapse because of May’s lack of authority in what are bound to be many months of tough and complex talks. A leading Christian Democrat ally of the German chancellor Angela Merkel – the MEP Elmar Brok – told the Observer that the chances of a collapse in the talks had significantly increased. “The British people saw through her [May]. The negotiations have become more difficult because Britain has not got a government of real authority,” he said.

May went to the country asking for a mandate on Brexit only to lose her Commons majority. In an intervention that will alarm hardline pro-Brexit Tories, the former foreign office minister Alistair Burt, backed by ex-education secretary Nicky Morgan and other pro-EU Tories, said Brexit could only be agreed and delivered if

the Conservative minority government built cross-party support behind a plan that would unite politicians and the country.

Burt told the Observer: “The new composition of the Commons knocks on the head the idea that the negotiations should be solely in the hands of the Conservative party. The government must lead them, and you cannot negotiate by committee, but it should now demonstrate that it has a sounding board for parameters consisting of senior parliamentarians across the parties, and some leading business and agriculture figures, for example.

“This would demonstrate to the EU that what had seemed a weakened position, with the loss of a majority, had been transformed into a stronger position, in which a sense of national endeavour was shown in the degree of agreement for its position. Doing this would enable the government to move forward with its timetable, with a sense of backing from public and parliament.”

In another intervention from the Tory side, Morgan, writing in the Observer, added that “to get Brexit and major policies such as social care funding delivered, the government will now have to build a consensus across the House of Commons and it will need to compromise.” Morgan says May’s determination to reject the single market needs to be re-examined as a priority.

In the same spirit, Labour’s Yvette Cooper called for a cross-party commission to run the negotiations and a transparent process to build a consensus: “It was always a mistake by Theresa May to try to conduct the Brexit negotiations through a small Tory cabal. This is the biggest issue for our country for a generation and if the deal is going to be sustainable it needs cross-party support and a broad consensus behind it. Now it is more important than ever. There is neither strength nor stability in a narrow, bunkered one-party approach, you need to include people with different ideas to get the best deal and widest support.”

Cooper added that it would be impossible to drive through the expected nine separate Brexit bills, on issues as wide-ranging as immigration policy, the right of EU citizens and trade, on the whim of a weakened prime minister in charge of a minority administration.

“In a hung parliament, you can’t possibly try to run the Brexit negotiations through a Theresa May-led Tory cabal. The whole thing will just fall apart. We should set up a small cross-party commission to conduct the negotiations, and have a clear and transparent process to build consensus behind the final deal.”

The Observer has learned that May took the fateful decision to call the election having been urged to do so by commission president Jean-Claude Juncker.

Theresa May and Jean-Claude Juncker at the European Commission headquarters in Brussels in October 2016. Photograph: Yves Herman/Reuters

It is understood that Juncker had advised May to call an early general election as a result of his concerns that the 17-seat majority she had inherited from David Cameron would not be enough during the pinch points of the negotiations, including over the issue of the UK’s divorce bill, estimated to be as much as €100bn.

“During bilaterals, in the margins of summits, Juncker repeatedly told her he thought she should do it,” one EU source said. A second European diplomat added: “People don’t understand. We want a deal more than anyone. We are professionals, we have a mandate to get a deal and we want to be successful in that.”

Juncker’s chief of staff, Martin Selmayr, made clear his reading of May’s failed election bid on Twitter, retweeting one German journalist who wrote: “Cameron wanted to secure his power and got the Brexit. May wanted to secure their power, and screwed up the Brexit. Strange”.

Concern over the implications for Brexit of May’s sudden loss of power and authority was also expressed by a senior government source who said he could not now see how she could drive the series of Brexit bills required, and the hugely complex and lengthy Great Repeal that will transpose EU into British law, with the current level of political instability and new makeup of the Commons. “We are in a completely appalling position. I cannot see a way through this.”

Former Tory cabinet minister Stephen Dorrell, now chairman of the European Movement, a pro-EU group, said: “At the beginning of the general election campaign, Theresa May said she was seeking a mandate to negotiate her sort of Brexit; the result denies her that mandate.” He added: “The prime minister’s version of Brexit was set out in the Conservative election manifesto; it said that sovereignty was a red line, and concluded that Britain must withdraw from both the single market and the customs union. In doing so, it threatened our economic interests, and funding for our public services.

“At a time when many families have seen no improvement in their living standards for more than a decade, and public services are grappling with rising demand and squeezed budgets, voters concluded that these priorities were simply perverse and refused to endorse them.

“That will require parliamentarians to maintain an open mind; they will need to question the negotiating mandate developed by ministers and they will need to make it clear to ministers that they cannot take support for granted at the end of the negotiating process.

“Most importantly, despite anything the prime minister may say, it is essential that parliament maintains for itself the option of voting for Britain to remain a member of the EU if it becomes clear that this is the best way to secure Britain’s national interest.”

May – who yesterday parted company with her two chiefs of staff, Fiona Hill and Nick Timothy, the man seen as framing her anti-single market approach – has insisted that the Brexit negotiations will start in a week’s time as planned. However, the EU neither knows who it will be negotiating with, or over what.