The currency fell 1% against the dollar in early trading to $1.6159, and also fell almost 1% against the euro to 1.2480 euros.
It came after a YouGov poll suggested supporters of an independent Scotland had taken a narrow lead in the referendum debate for the first time.
Just a week ago sterling was trading at $1.66 against the US dollar.
Shares in Scottish-based firms dominated the top fallers on the stock market. Edinburgh-based Standard Life fell 3%, Royal Bank of Scotland slipped 2.4% and Lloyds Banking Group, which owns Bank of Scotland and Scottish Widows, dropped 2.7%.
Perth-based energy supplier SSE, Glasgow pumps specialist Weir Group and fund manager Aberdeen Asset Management also all fell between 1.5% and 1.9%.
“The latest poll is a big wake-up call for all the investors who had not yet priced in the risk of a vote in favour of independence,” said Alexandre Baradez, chief market analyst at IG France.
Voters in Scotland go to the polls on Thursday, 18 September, when they will be asked the “Yes/No” question: “Should Scotland be an independent country?”
The poll, which featured in the Sunday Times, suggested that – of those who had made up their mind – 51% would vote to leave the UK, compared to 49% who would vote not to.
There is considerable uncertainty surrounding what currency arrangements an independent Scotland would make, with politicians in Westminster saying a formal currency union would be impossible.
Scotland could use the pound informally without control over policy in any case – as it could do with any other currency.
Barclays said in a research note that the vote for independence was just “the opening chapter”.
“[There will be] uncertainty over issues ranging from the timelines for political and economic independence, resultant institutional frameworks, lender of last resort for Scotland, the division of assets and liabilities, fiscal impact and policies, and what currency choices Scotland will have available and choose,” it wrote.
The BBC’s economics editor Robert Peston said that “the longer the uncertainties persist, the more prolonged the UK will suffer from an elevated cost of finance, and the greater the harm there will be to economic growth – both sides of the border.”