The UK needed to accept the four pillars of the single market, including free movement of labour, if it wanted to remain in the trading area after withdrawal, said Jean Claude Trichet.
“We know in advance that we have quite a long period of uncertainty and I would call for that period to be as short as possible, and for the position of the British government to be as clear as possible, as soon as possible,” he told the BBC.
Former Irish prime minister, and ex-EU ambassador to the US, John Bruton also criticised London’s failure to prepare for Brexit.
“I think there is a lot of surprise in other European countries that the government, which decided in its manifesto that it would have a referendum, hadn’t prepared in advance what it would look for once it left, given that there was always going to be a possibility that was going to be the result.
“One would have thought they would have prepared in the event that the people voted to leave,” he told the BBC.
Former Italian prime minister Mario Monti warned that giving Britain a “full Monty” deal without free movement of labour could destroy the single market as other nations demanded special treatment in certain areas as well.
The rebukes came as Theresa Villiers said it is “crucial” that the border between Northern Ireland and the Republic remains open and unfortified.
The former Northern Ireland secretary, who quit front bench politics after declining Theresa May’s offer of another Government position, said there was a reasonable chance of keeping the crossing between the two countries open despite the Brexit vote.
Ms Villiers told the Murnaghan programme on Sky News that there had never been a “truly hard border” and that softer measures could be taken to combat illegal migration.
“What has encouraged me since the referendum result is that we have the new Prime Minister, the Brexit secretary, we have the Taoiseach in Ireland all saying we need to keep this border open - it is crucial.
“If you have both countries determined to keep the border open I think there must be a reasonable chance that we can do that.”
Concerns about whether the free movement of people and goods will be impacted after Brexit have dominated the political discourse across the island since the vote.
The MP for Chipping Barnet said there were “plenty of ways” to “crack down” on those who do not have the right to work in the UK without the need for “physical border checks”.
“Of course we’d need measures to control EU migrants who came to the UK and chose to work if they didn’t have appropriate entitlements but we’ve already got legal mechanisms to deal with that because we’ve criminalised working without proper permission,” she told the programme.
“The best way to enforce rules of immigration is not through physical border checks at our land border with the Republic of Ireland, because as I say that’s never been a properly enforced border, no one wants it on either side of the border to become a hard border again.
“There are other ways in which we can deal with the risks around illegal migration.”