It is hard to think of a legal ruling with bigger political consequences than the one the lord chief justice and his colleagues handed down in the high court on Thursday. As a result, the May government’s secretive Brexit strategy will have to be rethought to comply, parliament will have to stop cowering in the corner about the referendum as it has done too often, while the welcome likelihood of MPs using their influence to ensure some form of “soft Brexit” has dramatically increased – as the immediate response to the news in the markets showed.

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Indeed, the political possibilities may go a lot further. The next general election is now much more likely to be a verdict on Theresa May’s Brexit stance, a prospect that ought to focus opposition party minds as well as the prime minister’s. That election could now take place earlier than May had originally intended. A second vote on the eventual Brexit terms, either in parliament or even another referendum, is also more likely. It’s even possible that Brexit itself just got a bit less inevitable. That’s still a distant prospect, but maybe it’s worth a little flutter.

The judges have done something else. By asserting that the UK parliament has sovereignty over a treaty issue with domestic implications, the court was in fact merely restating a fundamental principle. The precedent on which the court drew went back to Sir Edward Coke in the early 17th century and to the bill of rights of 1688-89. This is why the ruling is unlikely to be overturned in the government’s appeal to the supreme court. It may even be strengthened.

That Thursday’s ruling was needed at all is a reminder of how much in the British political and democratic system still needs fixing. On the one hand the judgment reopens the issue of the medieval prerogative powers that ministers continue to claim for themselves over Britain’s place in an increasingly interconnected world. These powers have no place in an open 21st-century democracy.

After Iraq, no prime minister can in practice take Britain to war without the authority of parliament. After this ruling, no prime minister can secretly renegotiate one of the most all-embracing treaties, the 1972 European Communities Act, ever made by the UK either. This is progress.

On the other hand, the ruling dramatically underscores the uneasy evolving relationship between referendums and parliamentary democracy in Britain. If ever there were an example of the way referendums create at least as many problems and cause at least as much instability as they resolve, here it was.

Parliament is far from perfect, but it is a lot better at making good, stabilising decisions than referendums, which give too much power to a biased and bad media of the kind we have here. The case for the kind of root-and-branch constitutional rethink that Gordon Brown made on Thursday continues to be overwhelming.

Nevertheless, parliament needs to rise to the occasion. Parliamentary sovereignty is a phrase that is more used than understood, let alone exercised. If you need proof, look at the Brexiters’ response to the court ruling. If there is one thing that united all wings of the leave campaign this year it was the belief that Britain should make its own decisions and “take back control”. Unless it means rule by the Daily Mail, that means parliament is the sovereign lawmaker and judges decide what the law means – which is exactly what the courts have just upheld.

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But you would never think that from the Brexiter reactions, which would be laughable if they were not so disturbing and arrogant. Ukip funder Arron Banks complained about unelected judges and sabotage. Nigel Farage said it was a betrayal that would lead to a half-Brexit. Leadership contender Suzanne Evans said the judges should all be sacked. The supposed libertarian Conservative MP Dominic Raab condemned the claimants for going to law at all. Iain Duncan Smith said the courts should not tell parliament how to do its job – they didn’t, Iain. Doubtless tomorrow morning the bullying and triumphalist anti-European press will be in primal outrage mode too.

In many respects it is to parliament’s discredit that it has done so little to force the issue and protect its rights. Instead, it has taken Gina Miller and Deir dos Santos to stand up against those who believe the June referendum is the be-all and end-all of all discussion about the future of this country in Europe. Thursday was a noble restatement of the importance of parliamentary sovereignty, but parliament itself has done pathetically little to deserve the outcome.

That needs to change. With the exception of the Scottish Nationalists, who march to a different drum, most English and Welsh MPs have been browbeaten into feeling they can’t say much about the detail of Brexit for fear of being labelled anti-democratic. Now’s their chance.

They need to start by asking for information; demand a green paper about Brexit plans and options. Labour, in particular, has to focus on the issue far better than it has yet done. Every time shadow Brexit secretary Keir Starmer opens his mouth on the subject, though, there is a glimpse of the possibilities.

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May will not be able to duck this ruling. It is a big humiliation for her approach. She may be tempted to go for a quick one-off vote in order to minimise the problem. But the supreme court appeal, where judgment is likely to come in January, gets in the way of that strategy. If the opposition wins the Richmond Park byelection at the start of December, a leader who thrives on being in control will not want to look as if she is on the run. Meanwhile, keep an eye on George Osborne.

Until now, May has combined secretiveness with hinting that a tough negotiation stance on migration would make single market access difficult. That approach will not withstand the impact of the need to consult parliament. She must face the likelihood that both the Commons and the Lords will focus on securing single market access in ways that could split the cabinet and provoke resignations.

These things are real possibilities now, not daydreams. The courts have left May little alternative but to change course on the most important issue of her premiership.