Scotland's first Minister Nicola Sturgeon announced plans to hold the ballot in late 2018 or early 2019, once the terms of Britain's exit from the European Union have become clear.
Sturgeon told the BBC last week that an independence vote should be held in autumn 2018, the "earliest point at which a referendum would be appropriate", as the terms for the United Kingdom to leave the European Union will be clearer by that time.
Scotland's Brexit Minister Mike Russell has insisted no move should be made to "try and thwart" a move for a second independence referendum.
But if Mrs May refuses to approve such a vote, she could provoke a constitutional crisis.
"By taking the steps I have set out today, I am ensuring that Scotland's future will be decided not just by me or the Scottish Government. Politics is not a game", she added.
"The language of partnership has gone, completely", she said.
The SNP have launched a crowdfunding bid to support their bid for a second independence referendum, aiming to raise £1m in 100 days.
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The survey found little change in people's attitudes since the first referendum on September 18, 2014 - with 44% in favour independence, 1% remaining undecided and an unchanged 55% preferring to remain part of the UK. People have said they do not want to go back to the division of a second referendum, she said. "Another such referendum would split society and would cause enormous economic uncertainty at the worst possible moment".
The SNP leader said the independence ballot would take place between autumn 2018 and spring 2019 and would involve a simple "yes" or "no" option. Sturgeon said that any attempt to prevent Scotland from having another vote would be "tantamount to the United Kingdom government, having sunk the ship with the Brexit vote, trying to puncture Scotland's lifeboat as well".
"I am ensuring that Scotland's future will be decided by ... the people of Scotland", Sturgeon said in a speech at Bute House, her official residence in Edinburgh.
The British government must agree before a legally binding referendum can be held.
As of Wednesday afternoon, just over 120,000 people had signed the petition, which is nearly 25,000 less than the whole of Dundee, Scotland's fourth largest city.
Sterling is 0.45 per cent up against the dollar - unchanged by Ms Sturgeon's remarks that she was confident of holding and winning a second vote.