Lloyds Banking Group, which includes Halifax and Bank of Scotland, has plans in place to set up new “legal entities” in England if the Yes campaign is victorious.
The move would not affect customers but it would end a symbolic tie to Scotland which has seen the firm registered there for historic reasons.
The Royal Bank of Scotland is expected to announce a similar plan today, and pensions and insurance giant Standard Life has also advised investors it is “planning for new regulated companies in England to which we could transfer parts of our business if there was a need to do so”.
First Minister Alex Salmond said it was “nonsense” and “scaremongering” to suggest Standard Life would leave an independent Scotland.
But Treasury Financial Secretary David Gauke said: “Looks like an independent Scotland will have more pandas than banks or insurance companies.”
A Lloyds spokesman said the group - which also includes Scottish Widows, where Prime Minister David Cameron made his emotional plea for the union to remain - had been contacted by concerned customers, staff and stakeholders about its plans in the event of a Yes vote.
The spokesman said: “While the scale of potential change is currently unclear, we have contingency plans in place which include the establishment of new legal entities in England.
“This is a legal procedure and there would be no immediate changes or issues which could affect our business or our customers.
“There will be a period between the referendum and the implementation of separation, should a Yes vote be successful, that we believe should be sufficient to take any necessary action.
“As a group we are committed to supporting our customers across Scotland and the rest of UK.”
Treasury Chief Secretary Danny Alexander told BBC2’s Newsnight: “When a company like Standard Life says that it would, unfortunately, sadly, have to relocate its business to London that is not some sort of decision that they make lightly.
“They make it on the basis that they regard that as the best way to protect their customers under the new circumstances.
“When we hear Lloyds and other banks making clear that they would have to do the same, again that is not something that they say lightly.
“They say it having thought about it, having talked to their board and to the senior people in those companies.”