Mr Robertson's elevation to become Lord Robertson of Port Ellen, ahead of his appointment as secretary general of Nato, means that a by-election will be held in his Hamilton South constituency in Scotland, on 23 September.
The day is also the start of the annual conference of the Scottish National Party.
Downing Street has described as "nonsense" accusations that the date of the move was a direct attempt to manipulate the by-election.
'Running scared'
But SNP deputy leader John Swinney said the only reason Mr Robertson had been elevated to the Lords was so the by-election could be held during their conference.
He said: "This is a clear abuse of democracy - an abuse even of patronage.
"The fact that New Labour are resorting to such jiggery pokery shows just how worried they are about the by-election.
"New Labour are running scared."
Conservative chairman Michael Ancram said Labour was making "the best political advantage they can of what they hope is a difficult political situation in Scotland".
He told the BBC: "There have been many times in the past when the Labour Party has waited until Parliament has come back to call a by-election and I reckon there's no coincidence that this by-election is now timed from the start of the Scottish National Party conference.
"I congratulate George Robertson on his appointment as secretary general of Nato and I hope he does a good job there.
![[ image: width=150]](/olmedia/425000/images/_428961_reid150.jpg)
"But to say that a peerage is now being awarded as a tribute is to really totally undermine the concept of a reformed and effective House of Lords which I understood a Labour government was all about."
The Tories are also calling for the prime minister to name Mr Robertson's successor at the Ministry of Defence.
Scottish Secretary John Reid insisted the poll had been organised for the convenience of the electorate rather than Labour.
He said: "George Robertson merits this elevation.
"It does enable the people of Hamilton, rather than being in limbo for three months, to choose their representative earlier than would otherwise be the case."
A Downing Street spokesman said it was "complete nonsense" that there was "anything untoward" in the announcement.
'Honour and privilege'
![[ image: width=150]](/olmedia/425000/images/_428961_stott150.jpg)
Mr Robertson, 53, who takes his title from a village in the Hebridean island of Islay where he was born in a police station, said he was delighted.
He said: "I was very pleased to accept the prime minister's offer of a peerage following my appointment as secretary general of Nato.
"It is a huge honour and privilege to be elevated to the Lords."
It is understood he will not take the whip or vote in the Lords until after he has served his term as Nato Secretary General.
By-election writs are to be issued in both Hamilton South and in Wigan, the seat of Roger Stott, the Labour MP who died earlier this month.
The Scottish Labour Party has announced that Labour's candidate for the coming Hamilton South contest will be Bill Tynan.
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Ministry of Defence
House of Lords
Nato
Labour
Scottish National Party
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