The UK's two biggest mortgage lenders, the Abbey National and Halifax, have increased the cost of their home loans by 0.25%.
But neither would say by how much they would increase the interest rates for savers.
Abbey National was the first of the high street banks to respond to last week's rise in interest rates by the Bank of England.
Other lenders were expected to follow suit, with Halifax doing just that and raising its rates a few hours later on Monday.
Halifax said its mortgage rate would go up to 7.24% from 6.99% immediately for new customers and from 1 December for existing borrowers.
Savers' rates would also increase on 1 December, it said without giving any details. An announcement would be made later this month.
Criticism of savers' rate rises
Abbey National's new variable rate is also going up 0.25% to 7.24% for loans under £60,000, to 7.19% for loans in the £60,000-£99,999 band, and to 7.14% above that.
It also said savers' rates would be increased on 1 December, but declined to say by how much.
The Bank of England's Monetary Policy Committee raised interest rates by 0.25% to 5.5% last Thursday.
The move was partly blamed on a response to rising house prices - with double figure increases recorded in the year to October.
Buoyant demand
The MPC hopes that a rise in mortgage rates may reduce the buoyant demand from house buyers - and the fast rising prices they are willing to pay.
The mortgage lenders' announcement followed a survey which found that four out of 10 homeowners would not use their current mortgage lender again.
Mortgage companies have come under increasing pressure to make their products more flexible and easier to understand and compare.
They have also come under attack for speedily putting up interest rates for borrowers, while being much more sluggish in increasing rates for borrowers.