The electrifying moment could come when the Prime Minister makes a statement in the House of Commons on March 14, flanked by Cabinet ministers.
While nothing is yet set in stone, sources say Downing Street is ready to move with lightning speed if, as Mrs May hopes, peers give way gracefully on Monday night and pass the Bill empowering her to write to Donald Tusk, the president of the European Council, invoking Article 50 of the Lisbon Treaty.
Preparations are understood to be at an advanced stage, with her opening demands in the Brexit negotiation already drafted.
Although ministers have not been told to cancel trips at this stage, ministerial private offices are geared up to bring them back to Westminster if required.
A source said: “There are a lot of stars that need to become aligned - but if the opportunity is there, she will not delay.” Another source cautioned: “No date has been confirmed.”
Mr Tusk said yesterday that EU leaders will respond within “more or less 48 hours” of Mrs May’s letter, kicking off possibly the most complicated series of negotiations in British history.
If Mrs May does not act this week, her next window of opportunity will not come until March 27, which some advisers feel is dangerously close to her deadline of the end of the month.
She gave a hint in Brussels this week that she was in no mood to delay, saying it was “time to get on with leaving the EU”.
However there are Dutch elections on Wednesday and a Scottish National Party conference on Friday.
The timetable is tight for an announcement on Tuesday, because the Government is determined to reverse two amendments made by the House of Lords to the Bill authorising Brexit. David Davis, the Brexit Secretary, will open a Commons debate on Monday afternoon, culminating in MPs voting to send the Bill back to the Lords stripping out the amendments - one protecting the rights of EU citizens in the UK, the other requiring parliamentary approval for any deal with the remaining 27 EU states.
If peers restore the amendments, the ensuing parliamentary “ping-pong” would delay Article 50.
After the Lords approves the Bill, it will need Royal Assent, which experts believe could be obtained from the Queen within hours.