Scotland's First Minister dispatched a letter to PM Theresa May requesting a Section 30 order - the powers needed to hold a new vote.
Northern Irish voters also opted to remain, however the Welsh and English vote to leave swung the referendum in favour of an exit for all four territories.
Most Scots think Holyrood, not Westminster, should have the right to decide whether to hold a second independence referendum, according to a new poll.
The poll asked participants who "should have the right to decide if there should be a referendum in Scotland that would allow the people of Scotland to choose between Brexit and Independence".
Sturgeon wrote to the Prime Minister after the Scottish Parliament voted to back a second independence referendum.
The letter suggests Ms Sturgeon has accepted that Downing Street is not going to give its permission for another referendum and is already planning an alternative route, which she will lay out in the Scottish Parliament after Easter.
Sturgeon said the referendum should occur "no earlier than 18 months from now, when the terms of Brexit are clear".
A spokesman for Ms May said the British government would respond in due course, but ruled out discussions on a second secession vote.
"The Prime Minister says that now is not the time for a referendum - we agree with that".
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Opening the debate, Sturgeon demanded Westminster should respect the wishes of the Scottish Parliament.
The PM is sticking to her belief that a vote in the next two years would be "unfair" on people in Scotland because not all the terms about life outside European Union will be finalised.
"I hope that will be by constructive discussion between our governments".
"As you are aware, the Scottish Parliament has now determined by a clear majority that there should be an independence referendum", read the letter signed by Sturgeon.
Ms May's Downing Street office confirmed that the letter had been received.
Sturgeon said the Brexit vote is forcing Scotland out of the European Union against its will as 62 per cent of Scots voted in June to remain in the bloc.
Ms Sturgeon, who has previously said she suspects the United Kingdom government may use Brexit as a "power grab", said that refusing permission for a vote would "go against the very foundations of devolution".
The Scottish government released a photo of Nicola Sturgeon drafting the letter to Theresa May, with her feet curled up on a sofa at her official residence, Bute House in Edinburgh.