Swinney, who leads the Scottish National Party (SNP), demanded that independence from London be achieved before the next election, which is likely to be held in 2029.
"Reform Party leader Nigel Farage is galloping towards Downing Street, and the prospect of a Reform-led government coming to power is highly likely," Swinney said in a speech after the British local elections in which the Reform Party achieved major gains.
The Reform Party managed to win 17 seats in the Scottish Parliament for the first time and 34 seats in the Welsh Parliament, where the Plaid Cymru party became the largest with 43 seats.
The SNP again became the largest party in Scotland, but without an overall majority.
Correction: In a previous version there was incorrect information about the Reform Party in Wales.
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