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Greta Thunberg is a welcomed distraction for Brexit-wary MPs and newspaper headline writers. But the reality beneath the surface is that we have entered one of the most intensive phases of the Brexit process yet. Theresa May is now considering a new strategy: not to bring another meaningful vote, but to go full-monty for the Withdrawal Agreement Bill, the entire legislative package, as early as next week. 

Of course, the majorities in the House of Commons have not changed, and there is zero chance that she can pass this bill without the support of at least a good number of Labour MPs. Her calculation is complex. The broad idea is that the legislation, which is amendable, could pave the way to a customs union. The Guardian reports that May appeared to be working towards  the reluctant acceptance of a customs union during a cabinet meeting yesterday. The parliamentary process could serve as a mechanism to produce such an outcome without May having to commit herself.

For now, May is running a dual strategy - the other being the official negotiations with Jeremy Corbyn and his team. May and Corbyn distrust each other. Both sides accuse the other of delaying tactics. Labour will only agree to support the WAB if May first signals a willingness to compromise. The strategy to table a withdrawal bill without a formal agreement between the party leaders would be risky for May. She would then need to rely on Labour rebels to support the bill - essentially those in favour of the customs union but opposed to a second referendum.

The gamble is risky, but not irrational. Labour advocates of a customs union are not opposed to the WAB itself, as it only sets out the legal terms for the withdrawal leaving the future relationship open. For Tories, the massive incentive to pass this bill lies in the prospect of accelerating May's departure without the need for a messy leadership challenge. If the bill were passed next week the UK would cancel the European elections, assuming that Brexit would be completed by end-May as agreed with the European Council. 

If parliament were to reject the WAB in its second reading, the government would be legally prohibited from tabling it again during the current parliamentary term. But the big procedural attraction is that this process would allow MPs to table amendments. If the Commons were to support Kenneth Clarke's version of a customs union in the form of an amendment to the bill, it might be easier for MPs to pass the package. 

All MPs would have to consider the consequences of a rejection. Elections would become more likely. Many MPs on both sides would be losing their seats. Nigel Farage's Brexit party has had a tremendously successful launch. The new Change UK Party launched its European platform yesterday, but is unlikely to have much of an impact. And their MPs would be most vulnerable in a national election. 

The customs union is the most likely amendment to succeed. The second referendum will almost certainly be an option. The Daily Telegraph reports that Sajid Javid, the home secretary, said the outcome should not tie the hands of future governments, and suggested unilateral amendments to the actual bills itself - in others words a course of action that would legally invalidate the bill. Astonishingly, the Tories are once again talking about the Malthouse compromise, to which they seem to return like a drug addict.

Another important strand of the story is the increasing probability of a Tory leadership challenge. We reported yesterday that MPs returned from the Easter holidays with a renewed determination to oust May at the earliest possibility. The 1922 Tory backbench committee is currently holding meetings to discuss whether to scrap the rule that protects a prime minister from a subsequent leadership challenge for one year. The debate is whether to reduce the time frame to six months - which would make another challenge possible in June - or whether to scrap it altogether. While the committee is generally split between remainers and leavers, opinion seems to be moving against May because of the dreadful polling numbers. A decision may be taken today, ahead of a full meeting of all Tory backbenchers. 

So how do these various strands fit together? The decision to focus on the WAB itself makes sense to us in view of the increasingly certain leadership challenge. Eurosceptics who are hellbent on a no-deal Brexit might still reject the bill. They might bet on May being replaced with a Tory eurosceptic, most likely Boris Johnson. It is not clear that he could single-handedly deliver a no-deal Brexit, but the risk of it happening are clearly higher with a prime minister committed to such action. It was May who prevented a no-deal Brexit, not the silly amendments to take no-deal off the table. 

The process would pose an interest dilemma for Labour MPs. Even if the official talks with the government fail, Labour could still prevail in the amendment votes - perhaps with the tacit support of May. In doing so, they could kill off the second referendum, an issue that threatens the unity of the Labour Party. May needs about 30 Labour MPs to support her and no Tory MPs to desert her.