Both Jeremy Hunt and Sajid Javid insisted it should be at least 10 years before another referendum is held, flying in the face of the Scottish Government timetable that would see Scots head to the polls on the issue next October.
The First Minister hopes another vote will be held on October 19 2023, though this plan seems unlikely.
Scotland’s top law officer last week referred a Bill to the UK Supreme Court in a bid to ensure any attempt by the Scottish Parliament to legislate for a referendum was within its powers.
Now two men who could become Prime Minister have dismissed the plans.
When asked on the BBC’s Sunday Morning programme if he would allow another referendum, Jeremy Hunt said: “Not in the next 10 years.”
Mr Javid, responding to the same question in a later interview, said: “The last one was for a generation and the generation hasn’t changed, so no.
“Not forever, but not at least for a decade.”
Meanwhile, fellow leadership candidate Tom Tugendhat said the UK was more a Scottish union than an English one.
He said on BBC Scotland’s The Sunday Show.“Scotland has been essential to the union right from the beginning.
“In many ways, this is a Scottish union more than an English one.
“It’s all about the ideas that so many people across these islands have generated together and the way that they’ve spread around the world and develop the new form of liberty that we’ve seen spread over the last 70-80 years.
“These are in many ways Scottish ideas.”
When asked if the union was a voluntary one, Mr Tugendhat said “of course” it was and that there were no rules stopping one country from leaving.
He added: “What (the Tories) are saying, simply, is you can’t keep asking the same question hoping for a different answer.”
He went on to describe the recent push as a “cheap political play” by the SNP to distract from the fact they are “failing” on education and healthcare.
Pressed on under what circumstances he would grant the request for powers to be devolved to hold a referendum, the chairman of the Commons Foreign Affairs Committee said he would not be drawn on “hypotheticals in the future”.
On the same show, SNP deputy leader Keith Brown said granting the Section 30 order required for another referendum would be a “good start” in repairing the fractured relationship between the UK and Scottish governments.
He said: “One of the fundamental tests of (if the relationship can improve) will be whether they’re willing to recognise the will of the Scottish people.
“Whether they are now willing to say ‘of course we’ll have an agreed referendum’, that would be a very good start for whoever takes over.”
“Given the runners and riders that we know about, they’re all people that defended Boris Johnson, they’re all people who were complicit in the lies and depravity of his administration, so I don’t hold out a great deal of hope.”