The recommendation from the House of Lords Constitution Committee comes in its report on the constitutional implications of the Scottish independence referendum, which is published today.
The committee also says that the wider status of MPs for Scottish constituencies, in terms of their ability to take part in other Commons proceedings not relevant to Scotland, would have to be decided before the 2015 general election if there were a "yes" vote on 18 September.
The committee concludes that in the event of Scottish independence the remainder of the UK would be the "continuator" state and so retain its current international status and treaty obligations, as well as UK institutions such as the BBC and the Bank of England. Scotland would become a new "successor" state and would not have any automatic claim on those institutions.
The committee says there would be no constitutional or legal requirement for the UK Government to adhere to the Scottish Government’s proposed timetable for full independence by March 2016 and that they should not do so if that would undermine the interests of the rest of the UK.
Other issues covered in the report include:
The report warns of a risk of Scotland entering a period of "constitutional limbo" following a "yes" vote whereby the UK Government ceased to represent Scotland’s interests but arrangements were not yet in place for the Scottish Government to represent Scotland internationally.
If there is a "yes" vote the negotiating team for the rest of the UK should be a small team from the UK Government, rather than cross-party. That team should consult the official opposition and the Welsh and Northern Irish Executives.
An Act of Parliament would be required to give the Scottish Government power to negotiate with the UK Government following a "yes" vote; it should also set up the negotiating team for the rest of the UK.
If, in the event of independence, Scotland were to establish its own Supreme Court, justices with experience of Scots law would no longer be appointed to the UK Supreme Court, but serving Supreme Court justices with experience of Scots law should continue to sit until they retire.
If Scotland secedes from the UK, as the law stands peers who live in Scotland would have to pay tax in the rest of the UK in order to remain as members of the House of Lords. If they did not want to do so they would have to retire from the House.
Baroness Jay of Paddington, chairman of the House of Lords Constitution Committee, said:
"There has been considerable speculation about the position of MPs for Scottish constituencies in the event of a “yes” vote on 18 September. Our view is that, while they should continue to sit in the House of Commons until independence day itself, they should have no role in negotiating for the rest of the UK nor in scrutinising the UK Government on those negotiations. If they did it would be a clear conflict of interest as they are elected to Parliament to represent constituents in Scotland.
It should be made clear before the 2015 general election whether Scottish MPs would take part in votes which did not affect Scotland.
We urge the UK Government to put the rest of the UK’s interests first in the event of independence negotiations. The Prime Minister should feel under no obligation to conclude negotiations by March 2016. The Scottish Government’s proposed timetable has no legal or constitutional standing.
We are clear that, in the event of independence, the remainder of the UK would be the “continuator” state while Scotland would be a "successor" state. That would mean that the UK continued to be party to existing international agreements, while Scotland would have to enter into those agreements afresh."