The government has restated its commitment to leaving the EU's custom union – ahead of a symbolic vote on the issue this week.
Last Wednesday, the government suffered defeat on the EU Withdrawal Bill in the House of Lords on the issue of staying in a UK-EU customs union after Brexit.
And MPs will get their own chance to debate the issue on Thursday.
But a senior Downing Street source told the BBC the government's position would not change.
"We will not be staying in the customs union or joining a customs union," the source said.
BBC assistant political editor Norman Smith said Downing Street's move was an attempt to reassure Brexiteers worried about a U-turn following the Lords defeat and pressure from the EU.
A customs union is when countries agree to apply the same taxes on imports to goods from outside the union.
This means when goods have cleared customs in one country, they can be shipped to others in the union without further tariffs being imposed.
If the UK remains part of the customs union, it would be unable to strike trade deals with countries around the world.
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But supporters say it would help to keep an open border between Ireland and Northern Ireland.
Labour has called for the UK to join a new customs union post-Brexit, saying it would leave the current one but negotiate a treaty afterwards that would "do the work of the customs union".
But speaking on a visit to a business in the West Midlands, Mrs May said leaving the customs union would allow the UK to strike new trade deals around the world, adding that she was seeking a "frictionless" border with the EU.
Brexit-supporting former minister John Whittingdale told BBC News Thursday's non-binding vote would be "a piece of theatre" but would have "no significance at all".
But he predicted pressure for the government when the EU Withdrawal Bill returned to the House of Commons in the coming weeks, saying reversing peers' amendments could prove "more challenging".
More crunch votes are expected when Remain-supporting MPs try to amend the trade and customs bills to put more pressure on the government to negotiate a customs union.
By Eleanor Garnier, BBC political correspondent
Theresa May has made leaving the customs union central to her whole approach to Brexit.
Downing Street's decision to reiterate its long-held position demonstrates concern at the top of government.
This week's debate will be purely symbolic and will not tie the government's hands.
But it could give an indication of the opposition the prime minister might face in a crunch vote on the issue next month.
With sabre-rattling from both sides of the argument, Downing Street felt sufficiently worried to clarify its position overnight.
The House of Lords is continuing its examination of the government's key EU Withdrawal Bill this week.
Last week's amendment would not necessarily keep the UK in the customs union – but would commit ministers to reporting on steps to negotiate a continued union.
Meanwhile the Times reports that Theresa May is facing pressure from Brexit-supporting ministers on the customs issue.
The report focuses on one of the two possible options put forward by Mrs May last month that would involve the UK imposing the same checks as the EU when goods arrive at its borders that are destined for the EU.
The Times said Brexit Secretary David Davis, International Trade Secretary Liam Fox, and Foreign Secretary Boris Johnson were concerned this would "encourage Brussels to press for Britain to stay in a customs union after Brexit".
Mr Fox is due to speak about the opportunities of Brexit in a speech to the financial industry on Monday.
In comments released beforehand, he said: "We will work with old allies and new partners across the world, utilising the UK's economic strength and diplomatic prowess to forge new trading relationships.
"Ultimately, our task is to remove the unnecessary regulation, bureaucracy and red tape that inhibit the free trade in services.
"Whatever one's view on the referendum result, it must be acknowledged that, outside the EU, this country will enjoy a new degree of economic agility."