Theresa May is a prime minister who faces an enormous challenge to recast Britain’s relationship with Europe in the wake of the EU referendum vote. But the Brexit statement she gave to the House of Commons on Monday was based not on reality but on unreality. The picture of Britain and Europe that she painted for MPs following last week’s EU summit does not and will not exist. Mrs May’s Brexit Britain is a fantasy island.

The underlying fantasy is that Mrs May is the master of Britain’s fate in these negotiations. This is not true. It was the European Union, united, clear and principled in its approach, that shaped the first phase of Brexit talks, which came to an end last week in Brussels. It will be the same in phase two, which will begin shortly. The final deal about the future trade terms on which the UK leaves the EU will not be settled by March 2019. All that will be settled before that is what the EU in April called “an overall understanding on the framework for a future relationship”. As the EU then went on to say, any free trade agreement must “encompass safeguards against unfair competitive advantages through, inter alia, tax, social, environmental and regulatory measures and practices”.

Mrs May probably gets this by now. But a significant minority of her cabinet and her party either doesn’t get it or is recklessly determined not to have it. That is particularly true of the part of the Conservative party that sees Brexit as a deregulatory opportunity, for whom “taking back control” means scrapping as many business costs – taxes, regulations, pension obligations, workplace rights and employment protections – as possible. Reports at the weekend suggested that Michael Gove is leading a cabinet push for the UK to abandon the terms of the EU working time directive – which among other things ensures a maximum 48-hour working week. This is the opposite kind of Britain to the one for which large numbers of working-class leavers voted in 2016. They wanted more security, as they saw it, not less. They did not vote for the freedom to work more hours for less pay and fewer rights. But this deregulated country is the one the Brexiter right is determined to give them.

A second fantasy is Mrs May’s insistence that the two-year transitional period that she is seeking is an “implementation” period. This is a trick. In order to calm leavers, Mrs May pretends the framework will be agreed before March 2019 and implemented after Brexit between 2019 and 2021. This is not true either. The negotiation to produce a real trade deal will take place after March 2019, not before. There will be nothing to implement in 2019. That is why there were reports at the weekend that Mrs May is being pressed to stay on until 2021 to prevent trade talks being ruined. But by then the UK will have left the EU and a general election will be upon us. There is no way whatever that this can be the “smooth and orderly” Brexit that Mrs May claims to be overseeing.

The third great fantasy is in many respects the most dangerous of them all. This was embodied in last week’s European council decision on phase one. As Mrs May put it on Monday, Britain is committed to uphold the Belfast/Good Friday agreement, to maintain the common travel area with Ireland and, crucially, to avoid a hard border in Ireland. But these goals – all massively desirable – are not compatible with the UK’s departure from the single market and customs union, to which Mrs May remains committed. Any future regulatory divergence between the UK and the EU – between the UK and Ireland – can only create a dangerous situation on the Northern Ireland border with the republic.

It is hard to know which is worse: that Mrs May knows this and does not mind such an outcome, or that she knows it and is pretending to parliament and the public that it is not a problem. Either way, this is the politics of impossibilism and of circle-squaring. Either way, British politics is crying out for truth not fantasy on Brexit. But Mrs May will not and cannot provide it.