This is a major red line for Brexit supporters who believe it is essential that any final deal with the EU must allow the UK to develop its own independent trade policy.
A solution involving a customs union would avoid what is termed by some economists as a "rules of origin shock".
Without some kind of customs arrangement UK firms would be faced with the high costs of rules of origin certification, and would have to prove where their produce or products come from in order to avoid paying tariffs when exporting goods to the EU.
Turkey is the only country which has an arrangement similar to that put forward by the IoD. This is significant, because under the EU-Turkey deal primary agricultural products are exempt. Agricultural products are often a key bargaining chip in striking new trade deals.
According to the IoD model, primary agricultural products like raw milk, fruits, and cane sugar that gets imported to the UK for refining would "definitely be excluded" from a partial customs union under this scenario.
However, goods such as cars, chemicals and medical devices would be included.
On the issue of trading in services, which account for nearly 80pc of the UK's economic activity, the report said: "A free trade agreement would still be needed to cover arrangements relating to services, as well as areas in which the EU has made clear it wants a continued level playing field, in order to maintain any reciprocal preferential market access."
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The IoD's Allie Renison, author of the paper, said: "A new but narrowed customs union would facilitate the continued flow of goods across UK borders." She added that such a move would reduce the administrative costs of Brexit for companies integrated in supply chains with the EU. It would also restore the UK's ability to enter into its own trade negotiations with the rest of the world.
Renison said: "This is a pragmatic option that both affords the UK new opportunities and minimises the risk."
Whether food stuffs such as cheese and butter would be covered under the customs arrangement is "up for negotiation", Renison said. However, one would still expect them to benefit from continued zero-rated tariffs in trade with the EU, she added.
Richard Graham, a Conservative member of the Exiting the European Union select committee and a UK trade envoy, told The Daily Telegraph that he believed such a solution was "spelling out in a bit more detail" what the Government is already looking at.
Graham said: "In order to carry the vast bulk of the population with us the Government have to find a compromise." This solution would have to allow businesses to carry on trading with EU partners as much as possible, while also giving room to allow free trade deals.
A Government spokesperson said: "We set out our two preferred models in our Customs Future Partnership paper. Both of these options set out that we will not be in a customs union, allowing us to make our own trade deals across the world but while still ensuring trade with the EU is as frictionless as possible."
