Could banks really charge you for depositing your cash? The answer is yes they could, but no they probably won’t. But with the Bank of England likely this week to cut the base rate to 0.25per cent, within a whisker of zero, the spectre of negative interest rates has become the latest financial scare. With rates so close to zero, are there new dangers to our finances?

Taxpayer-owned Royal Bank of Scotland last week fired a warning shot, by telling its business customers that if interest rates go below zero, and become negative, the bank cannot guarantee that it won’t have to charge interest for accepting money rather than pay it out.

That prompted the Federation of Small Businesses to advise its members to shop around for a better current account if their bank threatened such tactics.

Campaigner Martin Lewis noted that the first bank to “break that taboo” for its personal customers would “face uproar”.

But despite the success of the new super-fast current account switching service, which guarantees a seven-day turnround, relatively few people can be bothered to change their bank.

Matt Sanders at GoCompare.com says: “The figures show that consumers are far less ruthless at ditching poor value from their current accounts than they are with their car insurance or their mobile phone tariff.

“It’s the complexity of picking an account which is truly fit for purpose that’s the main barrier to increasing switching.”

Savings accounts are already at bombed-out levels. Since October 2015 there have been 1,264 rate cuts on savings accounts compared to just 232 increases according to Moneyfacts, with many of the better deals being pulled from the market in recent weeks.

This month the Financial Conduct Authority published its latest ‘sunlight remedy’ report, highlighting the worst deals being offered by banks. The Post Office, for instance, pays 1.25per cent on newer accounts but only 0.1per cent to customers in some closed accounts.

Current accounts paying more attractive interest rates on balances could also be about to trim their offerings. Santander is said to be reviewing its 123 account and likely to cut the top interest rate from three to two per cent. Rival accounts could follow suit.

Rather than make cuts to savers and depositors too obvious, banks are likely to try to win more customers over to fee-paying accounts. Fees can always be lifted, as Santander showed when the 123 account fee rose from £2 to £5 recently.

The downward drift will surely encourage more savers to take the plunge into peer-to-peer saving, where you lend money to businesses and individuals on an online platform and are typically rewarded with rates of three to seven per cent. Even if those pickings are thinned slightly, the risks (savers are not covered by the Financial Services Compensation Scheme) may look worthwhile.

Ultra-low interest rates are not good for banks, which rely on making returns from the cash they hold, so the current environment could make it harder for small challenger banks to offer competition. Already, 11 of these banks have complained to the Competition and Markets Authority that they face an “unlevel playing-field” in competing with the big banks on mortgages, because they have to hold more capital to make the same loans.

But could mortgages go lower? Borrowers on the two-year fixed rates, which are now typically between one and two per cent, will see no change to their monthly repayments. But those with trackers, which follow Bank of England rates up and down, are likely to see their mortgages get even cheaper. If you are on a rate that is one per cent above base and are currently paying 1.5 per cent, it will fall to 1.25per cent if the Bank cuts as expected this week – or to one per cent if base rate was to slide to zero.

But don’t expect banks to introduce negative mortgage rates, and pay you for borrowing from them. New tracker deals are likely to be less generous, or set a floor on the rate that can be charged.

What about investments and pensions? The theory of ultra-low or negative interest rates is that they stimulate the economy, which also feeds through into stronger company earnings, better dividends, and higher share prices. It has not obviously worked in Japan or Europe, where some rates have already turned negative. The best strategy for UK investors is not to be too dependent on the UK economy, at least for the time being. Lloyds Banking Group, for instance, has been one of the worst performing shares since the EU referendum because of its UK focus, and last week signalled that this year’s special dividend – the big attraction for investors – may not be guaranteed.

Tom Stevenson at Fidelity Personal Investing says: “In this lower-for-longer interest rate environment, with rates likely to go even lower, equity income funds continue to be a rare source of yield. Global equity income funds in particular look attractive given their ability to allocate across various geographical regions."