(Adds Labour comment)
EDINBURGH, Nov 8 (Reuters) - Scottish Nationalists will seek "a progressive alliance" with the opposition Labour Party if an election next month results in no one winning an overall majority, but the party wants a second independence vote in return, its leader Nicola Sturgeon said on Friday.
Britons head to the polls on Dec. 12 for a snap election which Prime Minister Boris Johnson called to end the Brexit impasse, with polls showing the governing Conservatives ahead of Labour but by varying margins.
In Scotland, the Scottish National Party (SNP) already has 35 out of 59 lawmakers, with some pollsters suggesting they will make further gains, positioning them as possible kingmakers.
"If there's a hung parliament ... SNP MPs will seek to form a progressive alliance to lock the Tories out of government," Sturgeon said at the start of the SNP campaign in Edinburgh.
"The SNP is not going to be giving support to parties that do not recognize the central principle of the right of the people of Scotland to choose their own future," she added.
Scottish voters opposed independence in a 2014 plebiscite but then backed remaining in the European Union in 2016, which the SNP has used to try and boost support for secession.
The Labour Party has not ruled out a second independence vote but said on Friday it was not seeking deals.
"We're not in this to do anything other than win and we're not doing deals," said the party's Brexit spokesman Keir Starmer.
Senior Labour figures have left open the possibility of a new independence referendum and Sturgeon said the party was getting closer to her stance.
"Labour's position, I think, on this is moving in the right direction," she said. (Reporting by Russell Cheyne; writing by Costas Pitas; editing by Stephen Addison)