Major said any attempt to close parliament would put Queen Elizabeth, the UK's head of state, in the middle of a political and constitutional crisis.
"If her first minister asks for that permission, it is nearly inconceivable that the queen will do anything other than grant it", Sir John said.
As a constitutional monarch, the Queen's executive authority is created to sit above politics.
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".
Some in Johnson's team say his lead is all but unassailable, and would only be at risk if their candidate commits a major mistake, something, based on the laughter and applause from the studio audience on Tuesday, he avoided.
"Who chooses our ambassadors is a matter for the United Kingdom government and the United Kingdom Prime Minister, and I have made it clear if I am our next Prime Minister the ambassador in Washington stays because it is our decision", he explained.
Former British prime minister John Major said it would be unacceptable and against tradition to shut down Parliament, and he would seek a court ruling to overturn it if it happened.
"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.
The news comes a day after Mr Hunt and Mr Johnson faced each other for a head-to-head debate on ITV.
"I think everybody is fed up with delay and I think the idea of now consecrating this decision to the judiciary is really very, very odd indeed", he said.
And he issued a stark warning about the prospect of suspending Parliament in order to force through a no-deal Brexit - something Mr Johnson would not rule out. Major's suggestion is important because Parliament has repeatedly signalled its opposition to a no-deal Brexit, but has no obvious way of stopping it.
The pound was trading near its lowest level for more than two years on Wednesday (local time) even with better-than-expected readings on the economy, as fears about a no-deal Brexit grew stronger.
On Tuesday, lawmakers narrowly approved a measure that could make it harder for the next prime minister to suspend parliament.
Major said there was a risk that Britain would not be ready to leave the European Union in October, and that Johnson lacked leadership qualities.