Amid warnings that a no-deal exit could still take place "by accident" next month, Whitehall sources said that planning by departments including the Home Office and Environment department was at "full tilt".
Ten Cabinet ministers have signed a letter, organised by Andrea Leadsom, the Leader of the Commons, which insists that the UK must leave the EU no later than May 22, avoiding having to hold elections to the European Parliament.
The letter, whose signatories include Sajid Javid, Foreign Secretary Jeremy Hunt and Environment Secretary Michael Gove, warns that May must stand by Conservative manifesto commitments on Brexit, including pledges that the UK would leave the customs union. Failing to exit the tariff-free bloc would leave the country unable to strike its own trade deals with other countries.
Senior ministers believe the pledge, which May repeatedly insisted she would honour, could prompt her to call a general election as soon as April 8, if pro-EU MPs succeed in forcing her to adopt a new position.
But Tories in marginal seats fear a wipeout that could see Labour leader Jeremy Corbyn in power.
One Cabinet member said: "There is no one in the Cabinet who thinks she should lead us into a general election." Another Tory MP who also warned the party faced disaster with May at the helm even suggested they could refuse to support a motion brought by May to trigger an election.
He said: "We would be annihilated. How many of us would vote for that?"
Senior Downing Street figures believe a general election could provide the only way to break the Brexit impasse, running a campaign based on delivering the result of the referendum with the aim of obtaining a larger Commons majority.
Options still alive
• DEAL OR NO-DEAL: The official deal looks to be on life support, having been rejected three times. The EU has given Britain until April 12 to decide on another postponement. Without a delay, Britain will crash out of the bloc on April 13 NZT.
• DELAY AND SOFTEN: The UK could delay Brexit for at least several months to sort out the mess. Britain would have to participate in European Parliament elections in late May. EU Council President Donald Tusk has urged the bloc to give Britain an extension if it plans to change course and seek a softer Brexit that keeps close economic ties. Sticking to EU trade rules would limit Britain's ability to forge new trade deals. But a customs union would ensure UK businesses can continue to trade with the EU and remove the need for customs checks between Ireland and Northern Ireland.
• ELECTION AND/OR REVOKE: Britain's next election is scheduled for 2022, but the gridlock in Parliament makes an early vote more likely. Britain also can revoke Article 50 and remain in the EU, which could become more likely if the government changes.
• NEW REFERENDUM: Any Brexit deal could be put to the public vote in a "confirmatory referendum". The idea has significant support from MPs.
Analysis: Europe's big guns are one step ahead
By Peter Foster
It has been a feature of the Brexit process that the British side has often been so consumed with its own internal political wrangling that often it seems to barely notice what is happening on the other side of the Channel.
This week the European side will continue to get its ducks in a row for whatever comes next.
The crux of that conversation is how to manage the Irish border in the event of a no-deal, which is why French President Emmanuel Macron and German Chancellor Angela Merkel will this week meet the Irish Taoiseach, Leo Varadkar. Anyone in the UK who assumes that a no-deal Brexit is now off the table, should ask themselves why Europe's two most powerful leaders are both making time in their schedules for Varadkar in the same week?
Europe has no appetite for a no-deal, but equally has fast-diminishing confidence that a moribund British political system will be able to prevent it happening.
The British Government now has just 10 days to translate Parliament's clear 160-400 vote against a no-deal into a commitment to holding EU elections in May and a new Brexit plan.
A no-deal presents the EU with a political trilemma — balancing the need to show solidarity with Ireland, while supporting the Good Friday Agreement and "no hard border", and protecting the EU single market.
The British side has already said unilaterally that it will hold no checks on goods flowing from Ireland northwards across the border, producing what has been condemned both in Brussels (and among Northern Irish business leaders) as a "smugglers' charter".
But what will Europe do for goods flowing the other way? Where will it set the cursor for checks and controls? And how ready is Varadkar for the political fallout from the re-establishment of a border in Ireland?
EU member states want to know how Ireland will actually manage that external frontier if it comes to a no-deal. The EU talks warmly, in terms of solidarity towards Ireland, but the position is steelier than it looks.