But there are growing concerns about the impact of cutting ties with Britain's largest trading partner, and the possible risk to peace in Northern Ireland by introducing an Irish border in the event of a "hard" Brexit.
Former Cabinet minister John Whittingdale told BBC Radio 4's The Westminster Hour that defeats like the one the government suffered last week in the Lords over the customs union played into the EU's hands.
Next month, MPs will vote on an amendment to the government's Trade bill which seeks to keep Britain in a customs union with the EU.
The row follows Mrs May's humiliating defeat in the Lords last week, when peers voted for an amendment to a landmark piece of Brexit legislation in favour of remaining in a customs union with the EU.
MPs vote on a motion to compel the government to drop its policy on the customs union later this week.
The prime minister has insisted that the United Kingdom will leave the common tariff area so it can pursue free trade deals outside the EU.
Mrs May is on record as saying Britain will leave both the EU's single market and customs union as part of Brexit.
Mrs May is set to hold a meeting of her inner cabinet on Wednesday where Brexit-supporting ministers are likely to press the issue of leaving the customs union.
A new framework for the digital single market should be completed during Austria's presidency, but United Kingdom companies may be frozen out if Brexit negotiations go poorly, she said in an interview.
The Customs Union is the body through which all 28 European Union member states collectively negotiate global trade deals with other states, rather than as individual countries. "That position hasn't changed and Downing Street have been clear about that this morning", he said.
This would likely enrage Brexiteers, with No.10 reported to believe that worldwide trade secretary Liam Fox and foreign secretary Boris Johnson could resign.
Downing Street sources insisted there would be no backsliding over quitting the customs union with Brussels after reports that the prime minister was ready to take a softer line.
Mr Wilson said it would be "very unwise for the prime minister to show any sign of weakness" to European Union negotiators.
The Irish border is a key element of their case. They want current arrangements to continue during the transition period and then create a new deal for afterward.