The UK's biggest mortgage lender, the Halifax, is expected to raise its standard variable mortgage rate (SVR) from 1 May.
The Halifax said the rise - from 3.5% to 3.99% - was due to the higher cost of raising funds for mortgages from both savers and the financial markets.
On Friday, RBS raised the rate on two of its mortgages from 3.75% to 4%.
This affects 200,000 borrowers with RBS and NatWest offset mortgages and home loans from RBS's One Account range.
The changes come just a few days before the third anniversary of the Bank of England cutting its bank rate to a historic low of just 0.5%.
"Halifax has written to customers advising them it is raising the cap or maximum rate it could charge on SVR which usually signals an imminent rate rise," said BBC business correspondent Joe Lynam.
"If Halifax increases SVR from current 3.5% to 4% that could add £16 a month for those with around £70,000 still remaining, or £24 a month for those with £100,000 left.
"But for those on an interest-only SVR it could mean a sharp 14% hike in monthly payments."
The Halifax has been part of the Lloyds Banking Group since January 2009, which is now 40%-owned by the government.
It argued that its hand had been forced by market conditions.
"The change acknowledges that the cost of funding a mortgage in today's market remains significantly higher than the longer term average," the Halifax said.
"The increase to the rate reflects the fact that raising money through retail savings and in the wholesale markets is currently very expensive by historical standards."
Consumer groups have reacted angrily to the news.
"It's shocking, it's coming at a time when people need this thing least of all," said Marc Gander, founder of the Consumer Action Group.
"Banks have never had it so good. They are doing fabulously well and it amazes me that they can't decide to share some of the burden that the rest of us are sharing.
"If they are saying they have to pass on rising costs, why can't they pass some of the good times on as well as the bad times?"
He also said he thought it likely other lenders would follow Halifax's lead.
"They reckon their customers are like sheep and they themselves are like sheep.
"One takes the lead, and I am absolutely confident that the rest will see these guys get away with it so think they may as well follow."
But mortgage specialist Melanie Bien told the BBC she was not hugely surprised by the move.
"Borrowers will be bemused because interest rates are at their lowest that they've been for three years, and there's been no movement there, but the cost of borrowing in the money markets has gone up a bit - this is what Halifax, RBS and other lenders are saying and this is why they now need to put the SRV up," she said.
Ray Boulger, at mortgage brokers John Charcol, said the typical Halifax borrower was likely to have an outstanding loan of more than £100,000 and would thus pay considerably more than the lender had highlighted.
"If people have an interest-only mortgage their repayments will go up by 14%, regardless of how long their mortgage has to go," he said.
The Halifax pointed out that its new rate was still cheaper than the SVR of many rival lenders such as RBS, Santander, Northern Rock, the Co-Op and the Yorkshire building society.
And it said that many of its SVR borrowers would be able to transfer their loans to cheaper fixed-rate deals, at no extra cost.
"Customers who wish to transfer their SVR balance to a new product with Halifax, or another lender, would not incur an early repayment charge," the lender said.
An RBS spokesman said the rises were down to the higher costs they were incurring borrowing money, which they had absorbed for some time before opting to pass it on to some of their lenders.
The news come as families are facing ever-increasing costs of living across the board.
On Friday, record high petrol prices were announced - motoring organisation the AA says the average cost of a litre of fuel is now 137.44p, with diesel at 144.67p a litre.
Andrew Montlake of mortgage brokers Coreco said some Halifax borrowers would still be put under pressure by the increases.
"For many in the current environment, even a small rise in their monthly outgoings hurts in a disproportional manner than it may have done in more normal times," he said.
"There are many who are only able to keep the wolf from the door because rates are low and a move such as this could lead to an increase in problems and arrears."