Britain’s humiliation over its Brexit negotiations has been caused by a fundamental inability to resolve a conflict between the desire to leave Europe politically, but to remain economically, Pascal Lamy, the former head of the World Trade Organization, has said.

He also said he did not think it feasible for the UK to leave the EU without an agreement, since it would be so costly.

Lamy, one of the world’s greatest authorities on trade policy and head of the WTO between 2005 and 2013, said: “I think the Brexiters know that businesspeople, the Bank of England, customs officials, technicians at airlines or on intellectual property, financial markets, all know that leaving without a deal will be chaos. They know that but they want to play chicken, which is what I believe is May’s game. Everyone knows there is a cliff, but until the last minute you pretend that going down the cliff will not be a problem because fundamentally you do not believe it will happen.

“It is like nuclear deterrence, which is a form of stabiliser. On the edge of the cliff the UK will not jump, but ask for a bit more time or will ask to stop the clock. It will be too costly.”

He said the proximity to a breakdown in the talks was striking. “Brexit is like a Rubik’s cube – you have 23 minutes to finish and we are at minute 22 and the colours are not there yet and we are still trying to fix it.”

“The continent,” he argued, “is totally powerless to solve a domestic political problem within the UK, as shown by what has happened in Westminster. One-third will buy what May has tabled, one-third says it is too much and another third says it is too little. If this remains unchanged, there will have to be a second referendum or elections, whether you believe it is wise or not.”

“What is fundamental is how do you exit as much as possible politically and as little as possible economically. That is the basic question of Brexit.

Lamy also accused Labour of indulging the same half in, half out approach as the government, adding that their proposals on a customs union and access to the single market made no sense.

He said: “The Labour proposal is to stay in a customs union and have some sort of say about how it works and what sort of trade agreements the customs union can enter into with a third party. It is a political fix that I am very doubtful would work in reality.

“It’s one foot in and one foot out. One foot in the customs union with one foot outside of the single market, but the reality is that the real problem is not the customs union but the single market. Access to the single market is not the same as membership of a customs union.

“The real issue is not the customs union, but the single market, and the problem negotiating the border does not stem from the EU. It stems from the internal market. If the UK imports chlorinated poultry from the US, there has to be a border, because the EU does not accept the marketing of chlorinated poultry. This is why, in my view, the Labour’s customs union solution is only half-baked.

“It would be very uncomfortable for the UK to be part of the customs union with no vote.”

With Jeremy Corbyn travelling to Brussels on Thursday and insisting his plans for a soft Brexit could be negotiated with the EU in a matter of months, Lamy expressed doubts whether Brussels would concede to Labour’s proposal to be outside the EU, but still have a say over the EU’s trade deals.

“The Labour policy of customs union membership is about political expedience. It probably does not make a lot of sense technically, but politically it sounds like a soft Brexit.

“It seems to be a solution because most people do not understand the difference between the customs union and the single market. Remaining in the customs union sounds like it is a bit like remaining in the single market. It is probably an intentional, clever, confusion.”

He said the lack of political compromise by the factions in the UK could hardly be put at Brussels’ door.

He argued: “It has never been a negotiation between Brussels and the UK. It has been a negotiation within the UK on the only question that matters – once you Brexit, how thick is the border, plus of course the Irish issue that almost played no role in the referendum campaign.”