There are growing calls for a rethink of Theresa May’s Brexit stance in the wake of a hung parliament.
The Conservatives leader had sought to take the UK out of the single market and end freedom of movement, but her party lost its Commons majority.
Former Chancellor George Osborne said he did not believe a majority of MPs now back a “hard” Brexit.
The Confederation of British Industry plans to canvas its members regarding the implications for business.
Its president, Paul Drechler, said: “The CBI has been calling on both European and UK negotiators to put the economy and people at the heart of these crucial talks.
“With only days to go before Brexit negotiations begin, the UK needs to be quick out of the blocks and agree on transitional arrangements, guarantee EU citizens’ rights and shift the focus of formal talks to future trading relationships.”
Societe Generale strategist Kit Juckes said the option of leaving the EU without a deal was unlikely to remain on the table.
“We are going to do a deal, so Mrs May’s threat that ‘no deal is better than a bad deal’, where we revert to World Trade Organisation rules, is over,” he said.
However, Mr Juckes said the incompatibility of immigration controls and the freest possible trade with labour flexibility meant any change was a difference in “shades of a hard Brexit”.
Airbus, which employs around 10,000 people at plants in Filton and Broughton, reiterated its call for a “softer” Brexit deal.
Chief executive Tom Enders said that mobility between its European factories was crucial for the plane manufacturer.
“We are a company that obviously has an interest in a free flow of people,” he said.
While Mrs May is banking on the support of the DUP’s 10 MPs to form a government, she will also need the backing of the 13 Conservative MPs from Scotland – 12 of whom are newly elected.
Ruth Davidson, the Scottish Tories leader, campaigned for Remain in the EU referendum last year and said on Saturday she wanted cross-party support with “free trade and economic advancement at the heart of the Brexit deal”.
Mr Osborne told BBC1’s Andrew Marr Show that “if the [Scottish Conservative leader] Ruth Davidsons of the world are starting to flex their muscles, then in my view that’s a good thing”.
Defence Secretary Sir Michael Fallon said the government’s view on Brexit remain unchanged.
Labour leader Jeremy Corbyn told Andrew Marr that his party will put a “substantial amendment” into the Queen’s Speech to promote a “jobs first Brexit” and to guarantee the rights of EU nationals to stay in the UK.