The campaigner and businesswoman Gina Miller will launch immediate legal action to prevent Boris Johnson from shutting down parliament in order to drive through a no-deal Brexit against the wishes of MPs, the Observer can reveal.

Miller’s lawyers, Mishcon de Reya, have written to the likely next prime minister, saying that such a move would be not only “constitutionally unacceptable” but also unlawful, and would lead them to mount an urgent challenge in the courts.

Miller has assembled the same legal team, including the QCs Lord (David) Pannick and Tom Hickman, that successfully forced Theresa May in early 2017 to grant MPs a vote before triggering article 50, the process that set the clock ticking on the UK’s exit from the EU.

Her latest move will add to the drama as the country faces political and economic uncertainty with the approach of the latest Brexit deadline of 31 October.

In a letter sent to Johnson, seen by the Observer, the team at Mishcon de Reya make clear that prorogation of parliament – something Johnson has repeatedly refused to rule out – would involve the use of prerogative powers, which courts would seek to limit. “Such powers cannot be exercised in a manner which is contrary to fundamental constitutional principles,” they say.

The letter adds: “It would seriously undermine parliamentary sovereignty for you, as prime minister, to prorogue parliament to prevent it from considering whether to legislate to prevent a no-deal Brexit.

“You would be closing the doors of parliament to prevent it from legislating on the most important political issue of the day, when time is of the essence. In such circumstances it would be unlawful for you as prime minister to advise Her Majesty to prorogue parliament for the purpose of preventing parliament from considering the enactment of a law to stop the UK leaving the EU without a deal.”

You would be closing the doors of parliament to prevent it legislating on the most important political issue of the day Letter to Boris Johnson

Cross-party groups of MPs who oppose a no-deal Brexit are still hoping to find ways to block such an outcome, which could mean the UK having to apply for a further extension. But Johnson has said that the UK must leave the EU on 31 October “deal or no deal”.

While his opponent in the Tory leadership contest, Jeremy Hunt, has ruled out prorogation to prevent MPs blocking no deal, Johnson has declined to do so.

Miller said that she and her legal team were “absolutely ready to go” to prevent what she said would be an outrageous attempt to bypass parliament, the very institution that Brexiters said they wanted to restore powers to when they campaigned to leave the EU in the June 2016 referendum.

After a case brought by Miller that set a constitutional precedent and upheld parliamentary sovereignty, the supreme court ruled by a majority of eight justices to three in January 2017 that MPs and peers must give their consent before the government could trigger article 50 and formally initiate Brexit.

Last week the former Tory prime minister Sir John Major said he would be willing to go to court to seek a judicial review to stop Johnson proroguing parliament.

“I served in parliament for over 20 years. I’m very proud to have done so,” said Major. “I have huge admiration for our parliamentary traditions.

“I’m not going to stand by and see them disregarded in this fashion. It is utterly, utterly and completely the wrong way to proceed.”

He added: “Let’s strip away the jargon of proroguing and contemplate what this actually means. What it means is that a prime minister – prime minister Johnson, presumably – because he cannot persuade parliament to agree with his policy, will close down parliament so that he can bypass it until his policy comes into operation.

“Now, nobody has done that since the Stuart era and it didn’t end well. And it shouldn’t end well.

“You cannot and should not bypass parliament in this fashion. And I cannot imagine how anyone could conceivably think that is right.”