Theresa May will stage the make-or-break vote on her final Brexit deal on Tuesday 11 December after a marathon Commons debate in which the prime minister hopes to turn around the 89 Tory MPs who say they cannot support it, The Guardian reported.

The crucial vote will come at the end of a five-day debate, according to a letter sent out by Julian Smith, the chief whip, to Conservative MPs that was leaked on Monday afternoon.

Dozens of Conservative backbenchers have publicly declared they were unable to support May’s deal, voicing complaints about the customs backstop that would tie the UK to some EU rules if a long-term free trade deal could not be signed.

No 10 said it was well aware of the scale of the opposition. “The number of MPs that there are is well understood,” a Downing Street spokesman said, while insisting May was confident of winning the vote.

Confirmation of the timetable came as the prime minister discussed with her cabinet at a one-hour political session how she was going to sell her Brexit deal to MPs and the country at large.

The spokesman added: “Cabinet talked about the strategy we are going to deploy to win the meaningful vote.”

However, it is now thought unlikely that May will challenge Jeremy Corbyn to a television debate on the Brexit deal. The idea is one of a number of ideas that had been considered by No 10 but insiders said: “There are a number of ideas that haven’t got off the ground.”