SCOTS living outwith Scotland, in particular those serving in the Armed Forces, should be given the vote in the 2014 independence referendum, MPs said as they warned Alex Salmond not to use the SNP majority at Holyrood to rig the poll.

A report by the House of Commons Scottish Affairs Committee on the Edinburgh Agreement pointed out many Scots not currently resident in Scotland wished to vote in it; under current plans only those on the Scottish electoral register will get a ballot paper.

The MPs said: "For example, we understand of the 11 Scottish Olympic medallists, only one is reported to be resident in Scotland. We sympathise; the future of their country is to be decided while they are working for a few years in England or abroad."

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The committee – which has no SNP representation – acknowledged there were "real practical problems" in devising a way to allow Scots outwith Scotland to participate. However, it said: "It is disappointing Scots temporarily excluded from voting and who intend to return will not be allowed to vote. We would much prefer that a suitable mechanism could be found."

Estimates have put the number of Scots living south of the Border at 800,000. The committee focused on those serving in the Armed Forces, who, under present plans, would be banned from taking part "due to accidents of posting".

It said: "All service personnel who will be eligible to transfer out of the British Armed Forces into their equivalent in a separate Scotland should be entitled to vote. Those who may, in future, be asked to risk their lives for a separate Scotland should be able to vote for or against its establishment."

The committee also stressed how the process for holding the referendum had to be seen to be fair. It should be agreed upon at Holyrood on the "basis of wide consensus rather than a majority being used to ram through partisan choices". In response, the SNP said while the committee's report was "grudging", it was welcome that it recognised Holyrood was the right and proper place to determine the terms of the referendum.

The Commission will publish its recommendations on the wording of the question, donations and campaign finance ahead of an MSP debate.

Meanwhile a think-tank says the UK would demand a "near veto" over an independent Scotland's budget. Capital Economics claim Scotland would be left with little economic freedom if voters back independence.