In a four-page letter to the chairman of the 1922 committee of backbench Tory MPs, the international trade secretary claims the scenario would see the UK "on the menu" in Brussels, without any control.
Hinting he could quit the cabinet if the prime minister pursues such a policy with Labour in the ongoing talks to break the Brexit deadlock, Dr Fox claimed the UK "ourselves would be traded".
The letter is significant as a permanent customs union with the bloc is a key plank of Labour's Brexit policy, and likely a red line for Jeremy Corbyn in discussions with the government.
Brexiteers, however, vehemently oppose anything that could restrict the UK's ability to strike independent free trade deals post-Brexit.
In his letter, published by The Telegraph, Dr Fox sets out how the UK would lose control of trade policy due to losing its member state input to the formation and agreement of EU trade policy.
Speaking ahead of further talks between the government and Labour, the cabinet minister said the loss of power was "something that Labour does not presently seem to understand".
"We would be stuck in the worst of both worlds, not only unable to set our international trade policy but subject, without representation, to the policy of an entity over which MPs would have no democratic control," he writes.
"As I said at the  meeting, in such a scenario the UK would have a new role in the global trading system - we ourselves would be traded. As the saying in Brussels goes, if you are not at the table, you are on the menu."
The comments from Dr Fox also come after Robert Buckland, the government's solicitor general, admitted a customs union was the "most likely outcome" of the negotiations between both Ms May and the Labour leader.
“It’s not perfect but, frankly, in this particular hung parliament none of us can get perfection, we need to compromise,” he told the BBC on Sunday.
The minister added that “something approximating a customs arrangement or customs union would be the most likely outcome” of the process.
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