Millions of current account customers are being advised to consider their options, following an increase in fees, and changes in interest rates.
From Monday, monthly charges on the Santander 123 account - held by 3.6 million people - will more than double.
At the same time HSBC is cutting interest payments to customers on its range of cash Individual Savings Accounts (Isas).
Barclays also announced more cash rewards for those who switch.
The change in Santander fees - announced in September - will see customers paying £60 a year, instead of the previous fee of £24.
The charge for its 123 credit card rises from £24 a year to £36.
'Do the maths'
Last year the Santander account proved very popular, with more than 27,000 people switching to it in a single month.
But experts said that - even after the changes -it still offered relatively generous interest payments of up to 3% a year, and cashback of up to 3% on some household bills.
"Don't jump ship until you've done the maths," said Hannah Maundrell, editor in chief of advice site Money.co.uk.
"To put it simply, you need to look at how much you're earning in interest and cashback. If it's less than the new £60 a year fee you need to take it as a wake-up call to seriously consider your options."
Analysis: Simon Gompertz, Personal Finance Correspondent
This is a sign of how dramatically current accounts are changing.
For years there was little to choose from between banks - the accounts were described as free but paid no interest and had hefty charges for going into the red.
Now switching is easier and banks are jostling for business with offers of interest and perks but adding new fees as well, features which can change at any time.
Santander said it was raising fees because of the increased cost of running a bank, such as capital requirements and the government's bank levy.
It was raising the cost of owning a credit card because of new European limits on interchange fees - the amount that banks can charge retailers for processing payments.
But Kevin Mountford, banking expert with Moneysupermarket.com, said banks were simply trying to improve their profitability.
"Banks are trying to increase their margins, through stealthy changes in fees," he said.
'£220 to switch'
From Monday, HSBC is reducing the amount it pays to savers who hold HSBC Loyalty Cash Isas to as low as 1.19%, part of a continuing trend of falling savings rates.
Six of the UK's biggest lenders cut rates last month, and Santander will reduce Isa rates in February.
Indeed last week the Bank of England announced that average savings rates fell to a record low in December.
As a result, consumers looking for better savings rates have turned to current accounts, which can offer better deals.
Barclays has said it will double its cash rewards programme for those who take out an account this month.
Marks and Spencer is already offering incentives worth up to £220 to anyone who switches.