The Labour leader said there should not be another vote while the economic and health outlook was “so precarious”.
He attacked Nicola Sturgeon’s call for an independence referendum, in the ‘early part’ of the next Scottish Parliament, as “misguided”.
And he said Boris Johnson should rule out a second vote.
He added: “Given the damage and division this would cause, no responsible first minister should contemplate it – and no responsible prime minister would grant it.”
He did suggest that there could be another independence referendum in the future.
But that should not be held until there had been a “proper assessment of the costs, consequences and uncertainties of separation”, in a thinly veiled criticism of the independence white paper produced by the SNP in the run up to 2014.
Scottish Labour hopes to revive its fortunes north of the border by going into May’s Holyrood elections with an avowedly Unionist message.
The once dominant Scottish Labour party is now in third place at Holyrood, behind the Conservatives.
Winning many more Scottish seats at Westminster is also crucial to Sir Keir’s hopes of becoming prime minister after the next election.
In his speech Sir Keir told pro-independence supporters in Scotland he was “not surprised” at polls which suggest rising support for a break-up of the UK
“Under my leadership we will do everything we can to win back your support for Labour and the UK. I know it won’t be easy,” he added.
He promised a new phase of devolution across the UK, saying he wanted to “push as much power as possible away from Westminster”.
