"Eyebrow-raising" numbers of Scottish businesses are moving their money across the border and into English bank accounts, according to the Cumbria Chamber of Commerce.

Rob Johnson, the chamber's CEO, said he knew of significant numbers of firms transferring funds from banks registered in Scotland to those headquartered in England. "We know it's happening, but we can't give names," he said on Monday.

"It's inevitable that people would start to do this because uncertainty is something businesses can't handle … It's not about businesses being pro or against independence, it's businesses saying: 'There are some real issues here and we don't know what's happening.'"

He said he wouldn't reveal the volume of money transfers but said he had heard of "enough to raise an eyebrow" in the past two weeks and that the net losers were banks known to be registered in Scotland "It's as if everybody has suddenly woken up," he said.

The extent of the transfers was not necessarily visible in Carlisle and other border towns, Johnson added. "It's not small businesses nipping over the border with wheelbarrows of cash. These days you can do it all on your iPad. Only the banks know how much of this is happening, but we get a flavour of it because the banks are our members … I think all of this is being played down and not up. It's not in the banks' interests to play it up because it causes destabilisation, which they do not want."

Yet most banks in Carlisle admitted they had seen an increase in inquiries from north of the border. In the Skipton Building Society tellers said they'd had "eight or nine" older Scottish couples in over the last week.

On Monday afternoon a couple switched their money to Skipton from Royal Bank of Scotland; last Friday another pair from Glasgow made the 95-mile journey in order to move "significant" sums from their RBS account, said one worker, who asked not to be named.

"They were worried that if it goes 'yes' on Thursday there will be a run on the banks," she added.

Others, already Skipton customers but based with Scottish branches, asked for reassurance that they wouldn't lose their money in the event of a currency change or a bank run: they were told it made no difference as all deposits are held centrally.

Outside Barclays on Monday John Watson, 59, from Aberdeen, said he was seriously considering moving his money out of the Clydesdale bank. "I'm certainly thinking about it," he said, adding that he had checked all his paperwork at the weekend to see where the Clydesdale is registered. The answer: "St Vincent Street in Glasgow."

Last week the Clydesdale said it would join Royal Bank of Scotland by re-registering as an English company if the Scots vote for independence on Thursday.

A self-declared "definite no voter", Watson said he was worried about pensions and shareholdings. "I'm concerned that there could be a change in currency. I'm worried [the Scottish government] won't be able to underwrite deposits. There's too much reliance being placed on oil."

Last Friday Santander sent out a two-page fact sheet for all staff on Scottish independence, including scripted answers to commonly asked questions. Tellers are encouraged to tell panicked customers that Santander is already registered in London and that deposits are held centrally rather than at local branches; that the bank is registered with the regulator, the Financial Conduct Authority; and that it will remain part of the Financial Services Compensation Scheme, which guarantees deposits up to £85,000.

A Santander spokesman said its call centres and branches had dealt with a number of queries relating to independence "but not a deluge by any means".

Last week The Lawyer revealed that an unnamed Scottish legal firm had shifted its cash out of Scottish banks for fear that a vote in favour of independence could lead to a run on them.