The Labour leader said it is not up to party leaders to reduce the election to a “completely different constitutional question”. He insisted the "central question" for voters will be whether they want to continue with a Conservative Government or change to Labour.
Sir Keir made the comments at a launch event in Edinburgh for Mr Brown’s long-awaited report on constitutional reform. It calls for democratic overhaul of the UK, including the abolition of the unelected House of Lords.
Speaking to journalists afterwards, Sir Keir was repeatedly asked what his response would be if Ms Sturgeon’s plan succeeds and pro-independence parties secure more than 50 per cent of the vote in Scotland at the next general election. The First Minister argues this would provide a mandate for independence.
The Labour leader said the next general election is a choice between Labour and the Conservatives, but refused to directly address the question. He said: "It's not how I want to frame it versus how anybody else wants to frame it – it's a general election across the whole of the United Kingdom.
"The central question is going to be, do you want to carry on with a Tory Government or do you want to change to a Labour Government?
"And I know that there's an attempt to try to change it into an election on something else completely. It isn't an election on something else completely – it's a general election for the whole of the United Kingdom."
Pushed on the issue, he said: "It's a general election between carry on with the Conservative Government or change to a Labour Government. No amount of discussion by other people is going to change the terms of a general election.
"That is what a general election is all about – what government do you want to lead on the economy, on international matters, on security, on defence, on the conflict in Ukraine, on the health service, on the cost-of-living crisis, on the energy crisis?
"These are not issues that can be reduced by somebody else into a completely different constitutional question.
"That is what a general election is about – all those issues – and the idea that all of that is as nought and nobody is interested in those questions, we're arguing about something that Nicola Sturgeon defines in that way, is just to stand in the way of common sense of what a general election is about.
"It's about all those issues, and that's what the parties will put before the country as we go into that general election."
Earlier, Mr Brown told an audience at the Apex Grassmarket Hotel in Edinburgh that Labour would fight the next election on issues such as jobs and the health service.
He said: “The Scottish National Party may want to fight the election with a one-line manifesto. The Scottish National Party may want it to be a one issue election instead of a general election. We will do the opposite.
“We will fight on the social, economic, political and constitutional change that we will bring about in Scotland and across the United Kingdom. We will fight on jobs, on the health service on the future of technology, we will fight on the environment – we will fight on all these issues.”
It came as he unveiled Labour’s blueprint for a “New Britain”. Sir Keir hailed the proposals for political and economic devolution in Mr Brown’s report as “the biggest ever transfer of power from Westminster to the British people”.
At an earlier event in Leeds, he said a Labour Government would aim to abolish the “indefensible” House of Lords “as quickly as possible”, ideally within its first term. It would be replaced by an assembly of the nations and regions.
Speaking in Edinburgh, Sir Keir said Labour would now start a consultation process on the report’s recommendations so that the party is ready to implement the measures when in power, adding: “We will need to hit the ground running and do this from day one.”
The report advocates extra powers for Scotland and Wales, with restored and strengthened devolution in Northern Ireland. Scotland would be able to enter into international agreements in relation to devolved matters, the status of MSPs would be bolstered, devolution would get greater constitutional protection and there would be enhanced access to economic support through the British Regional Investment Bank.
It says there is a “strong case for pushing power as close as possible to people in Scotland, and consideration should be given to establishing new forms of local and regional leadership, such as directly elected mayors”.
Elsewhere, some 50,000 civil service jobs would be transferred out of London. The report also proposes new rules for politicians and civil servants, clamping down on MPs’ second jobs, with a “powerful” anti-corruption commissioner to root out criminal behaviour in British political life.
It aims to create a “New Britain” by rebalancing the economy to drive up living standards in some of the most deprived areas. There would be more local control over decision-making, with local government given more capacity to generate its own revenue with new fiscal powers.
A spokesman for the First Minister said: “Labour’s position is utterly hypocritical and merely underlines their anti-democratic credentials. They will claim a mandate for their constitutional proposals regardless of whether or not voters in Scotland endorse them, and yet they will simultaneously stand shoulder to shoulder with the Tories in blocking the cast-iron democratic mandate which exists for an independence referendum.
“That stance is simply unsustainable. People in Scotland want an escape from a chaotic Westminster and they will not get that from Starmer’s pro-Brexit Labour party – only independence will deliver the change needed.”
Scottish Conservative chairman Craig Hoy MSP said: “The SNP will never be appeased by more devolved powers – nothing short of independence will ever satisfy them and it’s naïve to think otherwise.
“Scotland already has one of the most powerful devolved parliaments in the world, and the SNP – at the same time as agitating for more powers – choose not to use many of those already at their disposal, most notably in welfare.
“The SNP Government have no interest in making the current set-up work. Nationalists have a vested interest in devolution failing, to push their case for independence.
“The present settlement strikes a good balance, and people in Scotland want their two governments to work together, especially when there are much more pressing issues to be focusing on, such as the global cost-of-living crisis and our struggling public services.
“While Labour try to meet Nicola Sturgeon half-way on the question of independence, only the Scottish Conservatives are standing up to the SNP and building a real alternative, focused on people’s real priorities.”