Only a small handful of banks have so far made the decision to pass on to savers the quarter point rise in interest rates.
Thursday's decision by the Bank of England to increase interest rates to 3.75% was the first good news for savers in years.
In the past, banks have been criticised for raising rates on mortgages, but delaying benefits to savers.
In a good move for savers, however, Nationwide said it would be adding half a point to its Individual Savings Account - double the Bank's increase.
Savers will be eagerly awaiting announcements by banks and building societies over the next days and weeks.
Nationwide, Egg and Barclays are among a small number of banks who have so far announced changes to some or all of their savings rates.
HOW WILL IT AFFECT YOU?
The payment on a £100,000 mortgage will rise by £14 a month. Find out more
But many people will have to wait until at least Monday to see how their rates are affected.
Halifax, the UK's largest mortgage lender told BBC News Online it would not be announcing its new rates on Friday.
Its decision is quite unusual, as the bank normally announces changes on either the day of a rate decision or the following day.
A spokesman said most lenders were trying to find out what the indications were for further rate changes.
They also wanted to see how the money markets had reacted to yesterday's increase before it took its decision.
Falling interest rates have caused misery for many of Britain's savers over the last few years.
Hardest hit have been the elderly, many of whom rely on their savings for income.
How much people will benefit from the rate rise will, however, depend on whether their bank passes on the increase.
Susan Hammums, savings manager at financial adviser Chase de Vere, hopes the big banks follow Nationwide's lead.
"Isas have taken the brunt of the cuts in recent years. It is the most popular savings vehicle, and we are hoping other banks will follow its lead," she told BBC News Online.
Over recent weeks most of the banks have already pushed up their fixed rate mortgages by rises of up to 0.7%, in anticipation of a rate rise.
But over the next month, banks will announce changes to their Standard Variable Rate (SVR) deals.
Most of the major lenders, including Halifax, Abbey, Barclays and the Royal Bank of Scotland Group, were still reviewing their rates on Friday.
As well as acting as the bank's standard mortgage rate, the SVR normally influences the price of tracker and discount mortgages.
During Friday a growing number of lenders were announcing changes to their variable rates.
First Direct had added a quarter of a percentage point to its SVR, from 4.5% to 4.75%.
Cheltenham & Gloucester has also added a quarter of a percentage point, which will increase its SVR from 5.5% to 5.75%.
Sainsbury's Bank and Mortgage Express said they would be raising their tracker mortgage rates by the full 0.25%.
HSBC said it would be increasing its Home Buyer variable rate - its SVR - by 0.25% to 4.74%.
The bank said two-thirds of HSBC's savings customers would benefit from the full 0.25% rate rise.
However, the remaining savers will not receive the full benefit of the rate rise.
They will receive an increase of between 0.1% and 0.25%.
Nationwide, which is being generous to some of its savers is not being as kind to all of its mortgage customers.
Saving account changes
Egg Online Savings up 0.25% to 3.75%
Barclays Tracker Savings up 0.25% to 2.55%
Nationwide Cash ISA up 0.50% to 4.00%
HSBC accounts up by between 0.1% and 0.25%
It has pushed up its SVR by 0.35%, increasing its "Base Mortgage Rate" to 4.89% for both new and existing borrowers from 1 December.
The move will add an extra £20 a month to a £100,000 repayment mortgage, which is being paid back over 25 years.
The building society's tracker products, however, will move in line with the Bank of England's quarter point rise.
Pete Gettins, product analyst, at mortgage broker London & Country, said the decision to push up its Base Rate Mortgage by more than the base rate movement was "not a massive issue".
He said compared to other major lenders, Nationwide's SVR was very low - and its existing customers could always switch to a cheaper deal offered by the lender.