In the meantime, Brexit Secretary Stephen Barclay has been meeting members of the Alternative Arrangements Working Group of Tories drawn from all sides of the party who have been seeking a compromise solution to avoid the need for the controversial backstop.
While Mrs May questioned the move, describing it as "unclear", she did not reject the proposal out of hand and welcomed the Labour leader's desire to leave the European Union with a deal.More news: Manchester City sorry for playing Chelsea anthem after Etihad Stadium thrashing
But Stewart rejected this interpretation: "The prime minister remains very clear that she thinks that a very major economy like the United Kingdom needs to have the freedom to be able to make its own trade deals, so she's disagreeing with Jeremy Corbyn's suggestion that we enter a permanent customs union". He has also faced pressure from some of his MPs to push for another public vote on Brexit. Interviewed on BBC Radio 4's Today programme, Mr Johnson insisted staying in a customs union permanently would mean the United Kingdom being "essentially a colony'".
The existing Political Declaration, setting out the goals for the future relationship between the United Kingdom and the EU, "explicitly provides for the benefits of a customs union - no tariffs, fees, charges or quantitative restrictions across all sectors and no checks on rules of origin", Mrs May told Mr Corbyn.
However she questioned his support for a customs union with the EU, saying it would prevent Britain from striking free trade deals with other countries around the world.
"It is very clear from the European Union that non-EU members do not have a say in EU trade policy so to pretend that you could do so is a risky delusion".More news: USA warships again challenge China's claims in South China Sea
But she said it also recognises the development of the UK's independent trade policy.
She added: "The fundamental negotiating challenge here is the EU's position that completely frictionless trade is only possible if the United Kingdom stays in the single market". Instead, Parliament would be asked if it wanted to follow suit each time.
May's letter came amid a growing presumption that while she remains officially committed to putting a revised Brexit plan to MPs as soon as possible, in practice this is unlikely to happen before the end of February, if not later.
In a letter to Tory Party chair Brandon Lewis, the activists said any attempt to work with Labour to secure a deal or renege on manifesto commitments would be "catastrophic" for the party and lead to "severe electoral defeats" in the forthcoming May local elections.More news: NASA administrator says agency plans to go to the moon and stay