The monarch would be "in the midst of a constitutional controversy that no serious politician should put the Queen in the middle of", Sir John said.
Major said he believed a "queue of people" would challenge any prorogation in court.
"The whole of the diplomatic service will have seen that one of their most senior diplomats was prepared to be thrown to the wolves", Mr Major said on BBC Radio.
Major said the British parliament had been not suspended since the English Civil War when King Charles I have suspended it.
When Shelagh asked what Sir Alan would say if Mr Johnson said he was acting in Britain's interests by not upsetting Mr Trump, the Tory MP said: "Pull the other one". And I think it would be a rather curious thing to do if this is about taking back control to parliament, to actually shut it down.
Russell Westbrook Trade Imminent After Latest Oklahoma City Thunder Deal
As things are starting to heat up for the Thunder this offseason, let's look at five potential trade packages for the former MVP. No one player now on the trade block can replace PG, but perhaps an All-Star and several 3-and-D type guys can come close .
"I think it's very, very important not to envisage any circumstances in which we would fail to come out of the European Union on October 31", Johnson told a debate on ITV television in front of an audience.
Former London mayor Johnson raised questions over Hunt's commitment to leaving on the October 31 deadline while foreign minister Hunt criticized Johnson for relying on what he said was nothing more than optimism to win a deal.
Votes in parliament have indicated that a majority of MPs are against a no-deal Brexit because ofconcerns that it would cripple supply chains and damage trade.
In the debate Johnson said he would not "take anything off the table any more than I am going to take no-deal off the table".
On Tuesday, lawmakers narrowly approved a measure that could make it harder for the next prime minister to suspend parliament.
Sir John said there was a risk that Britain would not be ready to leave the bloc in October, and that Mr Johnson lacked leadership qualities. He followed other party grandees in questioning whether the former London mayor was fit for the highest office.
"National leaders look first at the interests of the country, not first at the interests of themselves and appealing to a particular part of a small electorate for a particular post, however important that post may be".