Liam Fox has been warned that his plan to prevent Brexit causing massive disruption to trade with the EU is probably illegal.

The World Trade Organisation (WTO) is unlikely to allow Britain to stay partly inside the EU’s customs union, a former UK single market adviser said.

Most business leaders are desperate not to leave the union, which allows exporters to sell into the single market without having to fill in forms or go through customs checks.

But, while staying in would cut costs and red tape, it would prevent Britain striking separate trade deals with non-EU countries – a key Brexit demand.

At the weekend, Dr Fox, the International Trade Secretary, floated the idea of staying “in part of the customs union, but not in other parts”. He pointed to the example of Turkey, which is inside for the sale of goods, but not for agriculture, services and procurement.

But Sir Andrew Cahn, who advised on setting up the single market in the 1980s, said what Dr Fox envisaged would be far more controversial. Britain appeared to want exemptions for the specific economic sectors in which it was strong, such as carmaking, aerospace and financial services.

Sir Andrew told BBC Radio 4’s Today programme: “Whether that would be legal under the WTO I doubt. Even if we got away with it, I don’t think the EU side would be prepared to do it. Why would they allow us to cherry-pick?”

The former chief executive of UK Trade & Investment (UKTI) said some sort of agreement was vital to prevent a hard landing when Britain leaves the EU, probably in 2019.

Citing lorries queued for several days at the India-Pakistan border, he said, of border checks: “They can get very extreme. That wouldn’t happen for us, but waiting for some hours and having voluminous paperwork to fill in is exactly what could happen if you are not in the customs union.”

Dr Fox is eyeing up a Turkey-style arrangement because it does not involve accepting free movement of people – Theresa May’s red line for the Brexit negotiations.

However, Ankara must accept all trading regulations decided by Brussels, common external tariff rates and the jurisdiction of the European Court of Justice.

Hinting at a deal on a partial customs union membership on the BBC’s Andrew Marr Show, Dr Fox said: “It is very important that we have continuity in our trade.”

The comments suggested a U-turn by the Trade Secretary, who, in July called for the UK to quit the customs union.

A key supporter of a hard Brexit – Iain Duncan Smith – has also dismissed the plan as contrary to WTO rules. He said: “You can't do that. Someone needs to tell them that. You cannot do sectoral arrangements. It is illegal.”

Nevertheless, Brexit secretary David Davis has revealed that officials are looking at 57 different sectors, as they weigh up single market or customs union access.