Brexit secretary David Davis has warned the UK would aim only for the "freest possible" trade with Europe compatible with migration reform.
Speaking at the Conservative party conference after Theresa May said she still wanted to secure free trade with EU members, Davis said it makes "perfect sense" for the UK to have the strongest possible ties with the nation bloc.
And he added: "History shows that the easier it is for us to do business together, the better it is for both Britain and Europe."
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Davis further noted that neither side would benefit from increased barriers to trade.
However, he also argued that last summer's Brexit vote represented an irrevocable demand for border reform and an end to freedom of movement.
"We want to maintain the freest possible trade between us, without betraying the instruction we have received from the British people to take back control of our own affairs," Davis said.
It represents the latest suggestion that the UK could quit the Single Market, and it comes after international trade secretary Liam Fox suggested last week that the UK would leave the EU's customs union, which imposes a common tariff on trade with external members.