The call has come from Conservative peer Lord Flight, who said that if Ed Miliband were to form a Labour government next year on the back of Scottish MPs following a Yes vote, then there would be political "mayhem".
The former Shadow Chief Secretary to the Treasury will air his concerns this week in the House of Lords through a parliamentary question on the "eligibility of Scottish MPs to stand for election in 2015 in the event of independence"; it will be followed the next day by a full Lords debate on the implications for the UK of the referendum.
Lord Flight stressed: "What happens in the event of a Yes vote as regards Westminster has not been provided for and needs to be provided for. It would be clearly wrong for a Labour government to be elected on the back of Scottish MPs if Scotland were to become independent."
The Tory peer argued "at the very least" Scottish MPs, following a Yes vote, should "not vote on English matters in the year they are still there" and said "consideration should be given that if there is a Yes vote in 2014, there should be no Scottish MPs in 2015; they come to an end next year".
Asked if he was suggesting all Scottish MPs should, in such circumstances, step down at the next election, he replied: "Correct."
If there were a vote for independence on September 18, Scotland would not leave the UK immediately. First Minister Alex Salmond has announced Scotland would become officially independent on March 24, 2016, with elections to the new Holyrood Parliament in May of that year.
This means Scottish MPs would not only continue to represent their Westminster constituencies up to the May 2015 General Election but for the 10 months thereafter.
Of the current 59 Scottish MPs, 41 are Labour, 11 are Liberal Democrat, six are Scottish Nationalist and one is Conservative.
Lord Flight made it clear that he believed Scots would reject independence in this year's poll, but wanted matters to be clear as to what happened at Westminster if there were a Yes vote. "We've heard nothing from the Government," he said. "We have to pin this down as much as we can."
Asked what he believed would happen if nothing was done and a Labour government was formed with a small majority based on Scottish MPs after a Yes vote, he replied: "The alternative is mayhem."
But Labour's Lord Foulkes rejected out of hand the Conservative peer's assertion. "It's nonsense," he declared. "Given the polls, a Yes vote is highly unlikely to happen. But if there were one, the UK would still exist and a lot of things could still happen. Independence would not happen straight away."
He added: "Mr Salmond says negotiations will happen in 18 months; realistically, it would be more like four or five years. Negotiations would involve the Houses of Parliament as well. Any legislation to set up a new Scottish Parliament in an independent Scotland has to be approved by the UK Parliament and any Scottish MP or MSP would be able to put themselves forward to stand."