Alistair Darling has said he does not believe that Nicola Sturgeon will hold a second independence referendum "any time soon" because she does not think she would win.
Mr Darling, who led the Better Together campaign in the 2014 referendum, said talking about the constitution was a "smokescreen" distracting from everything else that is going on.
The Scottish Government has launched a consultation on a new draft Referendum Bill, with Ms Sturgeon insisting voters north of the border should be given the chance to consider the issue afresh after the Brexit vote.
While the UK narrowly voted to leave the EU, almost two-thirds of Scots who took part in the ballot wanted to remain part of the bloc.
Downing Street has insisted that the Holyrood government has no mandate for a second referendum after independence was rejected in 2014.
Ms Sturgeon has said Scots should have the ability to reconsider the independence issue in light of the vote for Brexit, and to do so before the UK leaves the EU.
However, Mr Darling said he does not believe Ms Sturgeon will trigger a second independence vote soon.
The former chancellor told Scotland on Sunday: "I think everybody knows that if she thought she could win a referendum now she would hold a referendum tomorrow.
"Talking about the constitution is a great smokescreen for everything else going on.
"I don't think she will hold a referendum any time soon because she doesn't think she can win it. So why not get on with what she was elected to do and govern Scotland?"
He added: "I am very clear that we were told this was a once-in-a-generation decision two years ago, so it is.
"Remember, the decision was far more decisive than the European referendum if you look at the margins. It is time people said to the SNP, 'It is quite clear you don't think you can win'. People don't want another referendum."
Prime Minister Theresa May will host the leaders of Scotland, Wales and Northern Ireland tomorrow to discuss the Brexit process and her Government's economic plans.
The Joint Ministerial Committee (JMC) will meet for the first time since the European Union referendum and Downing Street said the talks would discuss how the administrations in Westminster, Holyrood, Cardiff Bay and Stormont could work together to secure the best Brexit deal.
The Scottish First Minister wants her Government to take charge of migration, as well as being allowed to strike its own international deals, and she has warned Theresa May that if her demands are not met and the UK pursues a so-called ''hard Brexit'', she will call a second independence referendum.
Former First Minister Alex Salmond told the Sunday Herald: "Unless Theresa May is prepared to listen and to accept the plan that Nicola Sturgeon is putting forward there will be another independence referendum in about two years' time. If I was Theresa May I'd tell my ministers to listen more to Scotland."