The former Tory PM thinks Mr Johnson suspended Parliament to push through no deal, and challenged this in court.
He said “Parliament might wish to authorise somebody other than the Prime Minister to communicate the UK’s intentions to the EU,” but cannot currently do so until mid-October.
Sir John argued it would be “remarkable” for the courts to decide they have no power over prorogation, as this could allow a prime minister to suspend Parliament at will to defeat opponents.
He said believing the suspension’s aim was to bring forward a new legislative agenda is “naive”, as no member of government has signed a witness statement to say this.
He is supporting an appeal brought by campaigner and businesswoman Gina Miller against an earlier ruling by the High Court in London that the prorogation was "purely political" and not a matter for the courts.
On Thursday, the third and final day of a historic hearing at the Supreme Court in London, Sir John's QC Lord Garnier said the intervention was "nothing to do with the arguments for or against Brexit".
Lord Garnier said his client had made “a clear and unambiguous allegation in evidence … that the reasons (for prorogation) set out in the documents put before the court by the Prime Minister cannot be true”.
He added: “Where an allegation of this kind has been made, it would be normal for there at least to be some kind of witness statement.”
There is a "world of difference" between dissolution and proroguing parliament: "The direction of power goes in different directions".
Sir John Major's lawyer says proroguing works for the PM, while dissolution works for the public.
Follow live: https://t.co/fDPhcIquAn pic.twitter.com/oAIScst1WI— Sky News Politics (@SkyNewsPolitics)September 19, 2019
In his submission he told the 11 justices that prorogation did not just stop Parliament from sitting, but prevented it from carrying out other functions – including its ability to find people in contempt.
He told the court people who have been found in contempt of Parliament in recent years included Mr Johnson’s senior adviser, Dominic Cummings.
In written submissions which were also provided to the court, Lord Garnier said the former prime minister is of the view the "inference was inescapable" that Mr Johnson's decision was "motivated by his political interest in ensuring that there was no activity in Parliament during the period leading up to the EU Council summit on October 17 and 18".
Lord Garnier, who served as solicitor general under David Cameron, added: "One of the central points of the present case - and the reason why these proceedings are necessary at all - is that the power of prorogation subverts the possibility of control by political means.
"Its effect is to deprive Parliament of a voice throughout the period of the prorogation.
"There is no possibility of political control except in the limited sense that a prime minister who exercises the power in a damaging way might face political consequences at some later date, when Parliament is permitted to reconvene.
"But where the effect of the prorogation is to prevent Parliament from discharging its role during a time-critical period, there is no possibility of meaningful political control of that decision until after the damage has been done."
Lord Garnier said it remains "genuinely unclear" whether Mr Johnson disputes that he was motivated by political interest because no witness statements have been provided.
He added that the submissions made on the Prime Minister's behalf at the High Court "studiously avoided committing to any clear position on the issue".
The barrister said the Supreme Court is under no obligation to approach the case on the "artificially naive" basis that the documents submitted on Mr Johnson's behalf should be "assumed to be entirely accurate and complete when even members of the Cabinet do not appear to believe them".
In a witness statement prepared for the High Court hearing, Sir John said it was "utterly unacceptable" for the Government to "seek to bypass" Parliament because it does not agree with the proposed course of action on a certain policy.
The statement read: "I served in Parliament for over 20 years both as a backbench MP and as a Government minister at Cabinet and more junior levels.
"I was of course Prime Minister for nearly seven years and am very proud to have been in the Commons and a minister.
"I have huge admiration for our Parliament and am a keen supporter of its rights and duties.
"I cannot stand idly by and watch them set aside in this fashion.
The Government's written submission the Government argues that if the court deems the advice was unlawful and that prorogation never happened, there would be nothing to stop it immediately seeking another prorogation for lawful reasons.
It adds that if the reasons were unlawful and the only available remedy in the opinion of the Supreme Court is to recall Parliament back immediately, then the Prime Minister would comply but would have to consider the timing of an earlier Queen's Speech.
It also submits the courts cannot preemptively stop a prorogation that has not yet been granted.
The hearing is due to conclude on Thursday afternoon, but it is not known when the court is expected to give its ruling.