On Thursday, with just eight days to go before the planned date for Brexit, exasperated European leaders granted Theresa May an extra two weeks to come up with an alternative plan, amid continued and total deadlock at Westminster. It was another humiliation for the prime minister who had insisted we would leave punctually on 29 March at precisely 11pm. On Saturday hundreds of thousands marched in London demanding another referendum – while a petition calling for Brexit to be stopped altogether passed 4m signatures. After another chaotic, tense and bad tempered week, what now for Brexit and Theresa May?

Are we still leaving the EU – and if so when?

Yes, probably, though it is unclear what the new date will be. On Thursday evening, the 27 other EU leaders agreed to delay the UK’s departure until 22 May – but only if May gets her deal through the Commons next week. The delay in these circumstances would be to allow enough time for Brexit-related legislation to be passed. If, however, May’s deal is rejected by MPs for a third time, or she doesn’t move it again, EU leaders made clear the UK would have to leave on 12 April. This would become Brexit day, unless another agreement on a longer extension is reached with Brussels. There is a big hitch with agreeing a longer extension, however, as there is no chance of signing up to one unless the UK takes part in elections to the European parliament scheduled for 23 May – which the prime minister is dead against.

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So what will happen this week?

On Monday a string of Brexit motions will be tabled, including one calling for parliament to take control of the process by holding a series of “indicative votes” two days later. This is an attempt to see if a parliamentary majority can be mustered for a different Brexit model, such as a Norway-style single market membership, or a permanent customs union. On Tuesday May could well put her deal to another “meaningful” vote (MV3). But if she thinks she is on course to lose again she may shy away. Parliament must vote by the end of the week on a statutory instrument (secondary legislation) to change the intended leaving date on the withdrawal bill from 29 March, to either 22 May (if May’s deal has passed) or 12 April if it hasn’t. It must do this before 11pm on Friday.

Is a no-deal Brexit still possible?

Yes, very much so. No one (except Brexit hardliners) wants no deal but it still could come to pass because there is no majority for anything else that would avoid it. Whatever new date is set for Brexit, no deal stays as the default position if parliament cannot agree how we should leave. MPs have twice voted down May’s agreement by huge majorities, and have not come close to agreeing any other plan. We will now leave with no deal on 12 April unless one of several things happen, none of which looks likely. Either MPs have to be converted in sufficient numbers to allow May’s agreement to pass (unlikely); or they have to find a majority for another form of Brexit (possible, but late in the day to try); or they have to back a longer extension which will mean holding European elections; or just shelve Brexit altogether.

Facebook Twitter Pinterest Some of the thousands of banners and placards. Photograph: Kirsty Wigglesworth/AP

Could the government and parliament decide to revoke article 50 and cancel Brexit?

Yes – and there are millions of people calling for this to happen. A petition demanding revocation has been signed by more than four million people. It was started in late February by “frustrated remainer” Margaret Georgiadou, but began to rapidly gain signatures on Wednesday evening. The UK can revoke at any time so long as it is still an EU member, even during an extension to its membership. But doing so remains unlikely as there is little support in parliament. Under government rules, parliament has to consider all petitions that amass more than 100,000 signatures and it is now certainly a hot topic.

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Could we still have another referendum?

Yes. Today’s huge march showed how wide support is. The problem is that there has been insufficient backing so far in parliament. Only a handful of Tory MPs from remain seats openly back the idea and plenty of Labour MPs in leave-supporting seats are against. The Labour leadershp has blown hot and cold about a second referendum for months, fearing a backlash from leave voters. Jeremy Corbyn has, however, suggested that Labour will back an amendment by two Labour MPs, Peter Kyle and Phil Wilson, that would deliver a second public vote if the right moment is found. Under their plan, MPs would allow May’s deal to pass on condition that there is a confirmatory vote in the country. Labour is worried about being seen to cause no deal and worried about being seen to help May land her deal. With Labour’s strong backing, a vote on the Kyle-Wilson plan, if tabled when the danger of no deal is at its height, could be very close.

Can Theresa May stay as prime minister if her deal is defeated yet again?

Not for long. May will by then have been defeated three times on the defining issue of her premiership and the most important one to have faced the country since the second world war. It was also the issue on which she called a snap election in 2017 only to lose her majority. She wanted her own mandate on Brexit and failed to get one. Tory MPs on the leave and remain sides of the argument now want her out this summer at the latest even if her deal gets through parliament. If she tries to go on beyond December, there will be another confidence motion by her own MPs, and she is unlikely to survive. The men in grey suits will have been hammering at her door by then. Her statement on Wednesday about MPs obstructing Brexit and playing political games was the last straw for many on her own side. She is on the way out.

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Could we agree an alternative form of Brexit?

Yes, possibly. The process of indicative votes will bring forward different ideas for a soft Brexit, including the Norway-style model of single market membership and close customs cooperation with the EU. Labour will also push its ideas for a permanent customs union. But the chances of forging sufficiently wide cross-party consensus are not high. Anything that looks like a Tory-led plan will put off Labour MPs and vice versa. No side wants to deliver the other side’s Brexit. An arrangement that keeps the UK close to the single market and in a customs union is possible if it could be presented as genuinely non-partisan. But MPs fear that the indicative votes will in the end just show that parliament can’t agree anything – if it could, it would have done so by now.

What is Labour’s policy now?

That is arguably the hardest of all questions to answer. In its last manifesto it said it would respect the result of the 2016 referendum. At its party conference in Liverpool last September it agreed to keep a second referendum on the table, with the option to remain being on the ballot paper, if all other possibilities had been exhausted. Since then the leadership has appeared one minute to back a second referendum wholeheartedly, while the next saying it is most interested in promoting its own Brexit plan and trying to force a general election. Keir Starmer, the shadow Brexit secretary who wants a second referendum and to stay in the EU, and Jeremy Corbyn, who clearly would rather not have a public vote and thinks we should leave, send out very different messages because they seem to want different outcomes.