The British government would have no say over new trade deals if it was in a customs union with the European Union, a former head of the World Trade Organization has said.

The comments from Pascal Lamy, who is also a former EU trade commissioner, will dent the hopes of MPs who favour a customs union but seek to retain British influence in the EU.

Jeremy Corbyn told the CBI conference last year that Labour wanted “a new comprehensive and permanent customs union with a British say in future trade deals”. Some Conservatives also favour a customs union with the EU as part of a possible solution after the government’s historic defeat in the Brexit vote last week.

Theresa May has ruled out joining a customs union, but the idea could return if she fails to win a majority for her plan B, a thinly modified version of plan A that involves asking the EU for concessions, which the bloc has repeatedly ruled out.

Lamy told the Guardian he did not see the UK having a decision-making role if it were in a customs union with the EU.

“To be frank, rather not,” he said. “That implies a degree of homogeneity within the customs union on what the purposes of a trade policy are, which would mean the UK’s economic system would remain aligned with the EU economic system, which is precisely what the Brexiteers don’t want.”

He said Labour’s plan for the UK to remain in a customs union with the EU was a sign that the party was seeking to “soften what is on the table” and achieve a less economically costly Brexit. “Reinstalling borders is costly and the fundamental equation of Brexit is how do we exit politically as much as possible but economically as little as possible,” he said.

The EU customs union, a common external tariff levied at the EU’s external border, one of the original aims of the European project, has been operational since 1968. The single market, launched in 1993, abolished internal borders within the EU and created far-reaching harmonisation of rules and regulations.

While a customs union would help solve the impasse over the Irish border, the EU would still require additional regulatory checks. One EU official said: “If [the British] want a customs union like Turkey, we can negotiate that; the problem is it will not solve friction. That is simply an illusion.”

If the UK were to seek a customs union, EU member states would look to bind the UK to some single market rules to avoid unfair competition.

Lamy described the customs union as a political construct based on compromise. “It is not that France and Germany and Italy always have the same preference for opening or less opening [of their markets], for cheese or cars, it is that they find a compromise between them, but they converge because they are part of a system that is about convergence.”

The EU created a customs union with Turkey in 1995, which Lamy said was a precedent to study, noting that the EU had never allowed Ankara a seat at the table. The customs union with Turkey covers industrial goods but not agriculture, services or public procurement. Turkey follows EU rules on industrial standards and is obliged to apply the EU’s external tariff to imports from non-EU countries.

This leaves Turkey with lopsided trading arrangements with the rest of the world. Countries that have a trade agreement with the EU, such as Canada, have preferential access to the Turkish market if their goods enter the EU, but Turkey does not have reciprocal access.

“There are always problems,” Lamy said. “The Turks are permanently frustrated that whatever trade agreement the European Union negotiates with a third party, they are onboard while they have no say.”

The former trade official described Brexit as “a mess that was to be expected”, and he compared the preference of leading Brexiters for trading on WTO terms to playing football in the fourth division. “It is not that you cannot play soccer in the fourth division, but it is not the way you play in first division.”

Under his football analogy, the EU’s internal market is league number one, customs union counts as the second division, a bilateral trade agreement is the third division, while North Korea plays alone in the fifth division.

David Henig, a former UK trade negotiator, said he did not expect Brussels to give the UK a seat at the table if the government sought a permanent customs union.

He predicted there could be constant irritants, citing a recent EU decision to impose tariffs on rice from Cambodia and Myanmar after a “safeguard” investigation requested by Italy, one of the EU’s eight rice-growing countries.

“Italian rice growers have been protected in the face of the poorest countries in the world,” Henig said. “It is going to be really difficult to maintain a customs union without a UK say when these sorts of things happen. And these things do happen.”