Alison Rose said an independent Scotland would be too small to support the banking group, which has been based in the Scottish capital since it was founded 294 years ago.
She said: “In the event that there was independence for Scotland our balance sheet would be too big for an independent Scottish economy.
“So we would move our registered headquarters, in the event of independence, to London.”
Mr Galloway said if the SNP win independence, people in Scotland would wake up “to find companies and high-net worth individuals had fled south of the border”.
He said: “Scotland’s deficit last week reached eight times higher than the permitted deficit for entry into the European Union. Eight times greater!
“That means in order to get into the EU, the SNP would have to Scotland’s deficit by seven-eighths.
“We are a country with a tax base so weak that we are barely able to fund the public services we enjoy today.
“The life we enjoy is funded by the Exchequer in London, that gives our people £2,000 per head more than the citizens of England and Wales.
The Savanta ComRes survey found that 54 percent of Scots support the Union, with 46 percent wanting to leave the UK.
The poll also found that support for the SNP has dwindled and that the party may lose two seats, falling four short of a majority.
Speaking about the recent Svanata ComRes survey, Chris Hopkins the associate director said: “The direction of travel has been clear in the last few polls.
“Support for both independence and the SNP dropping ahead of the May elections.”