The issue has been dominating the debate on the contours of Britains future relationship with the European Union (EU) as a non-member of the economic bloc and threatened May's own position as prime minister.
"It is not our policy to be in the Customs Union," a Downing Street source was quoted as saying.
The Customs Union allows the UK tariff-free trade within the EU and its continued membership after Britain has left the EU would inhibit the country's ability to strike its own deals with other countries, like India.
The Downing Street intervention last night came as the EUs chief Brexit negotiator, Michel Barnier, set off for Britain for a meeting with UK Brexit minister David Davis.
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Following his meeting in London, officials on both sides will be able to move on to focus for the first time on the transition phase or "implementation period" planned after Brexit in deliberations planned in Brussels next week.
Potential sticking points during this weeks talks include citizens' rights, with the UK insisting EU nationals arriving during the transition phase should not have the same rights as those who arrived before Brexit day March 29, 2019.
May is set to chair meetings with her Cabinet ministers on Wednesday and Thursday as her Brexit sub-committee decides the details of the UK governments policy regarding a customs union.
"I have a surprise for the Brexiteers...the committee that meets in order to help make these decisions is more united than they think," she said.
Rudd stressed that all sides were agreed on the need for "frictionless trade", the ability to strike international trade deals and to avoid a hard border in Ireland.
"We want to have a bespoke agreement. Now we're not going to surrender before we have that battle," she added.
A "partnership" arrangement would see the UK "align precisely" with the EU in terms of imports and exports, removing the need for any customs checks between the two.
The UK would continue to operate its own checks on goods coming from outside the EU and safeguards would be needed to prevent goods entering the EU that had not complied with its rules.
An alternative scenario would involve the UK extending customs checks to EU arrivals but under a "highly streamlined arrangement" to minimise disruption at ports and airports.
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