Downing Street has previously suggested he would fight the Act in the courts, but a final, dramatic showdown in parliament now appears to be the favoured option.
Votes could also be staged on whether to stage a Final Say referendum as the best route out of the crisis, or even on revoking Article 50 to cancel Brexit altogether.
Mr Johnson is unlikely to win a vote for a no-deal – he has yet to win a Commons vote on anything – but defeat would at least strengthen his claim to have been forced into an extension by anti-Brexit MPs.
It would be the first Saturday sitting since Argentina invaded the Falklands Islands in 1982 – and only the third since the Second World War.
The debate will also take place to the backdrop of another huge demonstration demanding a fresh Brexit referendum, expected to attract hundreds of thousands of people.
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Organisers said there was no question of plans for the demonstration being changed because of the Commons sitting, pointing out that permission has already been granted for the march and the rally in Parliament Square.
“It makes the march even more important than ever,” said a spokesman. “It makes the march absolutely pivotal.”
Mr Johnson is expected to meet Leo Varadkar, the Irish premier, on Thursday, but with no realistic hopes of a breakthrough to reach a deal.
In a TV interview on Tuesday evening, Mr Varadkar attacked the UK’s proposals for ‘two borders’ to avoid the need for the backstop, to guarantee no hard border.
“Essentially what the UK has done is repudiated the deal that we negotiated in good faith with prime minister May’s government over two years and have sort of put half of that now back on the table and saying that’s a concession. Of course it isn’t,” he protested.
David Sissoli, the president of the European Parliament, was also downbeat after meeting Mr Johnson in No 10.
“I came here in the confident hope of hearing proposals that could take negotiations forward. However, I must note that there has been no progress,” he said.
“As I explained to Mr Johnson, the parliament will not agree to a deal at any price. We will not agree to a deal that undermines the Good Friday Agreement and the peace process or compromise the integrity of our single market.”