Savers have been offered some hope as a wave of providers pledged to boost their rates.
Britain's biggest building society, Nationwide, said it would be increasing savings rates by 0.25% for all members who received a reduction of 0.25% as a result of the bank rate reduction in August 2016, including the Society's most popular products.
Yorkshire Building Society said it would add the full 0.25% rate increase onto its variable rate accounts, while TSB said it would also tweak rates on variable rate savings accounts upwards.
Santander has said savings products linked to the base rate will move in line with the increase.
HSBC said that while its savings rates are not directly linked to the base rate, it will be reviewing these in light of the Bank of England's base rate decision.
Lloyds Banking Group, which includes Halifax, has also said it will review its savings rates.
According to figures from Moneyfacts.co.uk, savings rates slumped after the base rate was cut from 0.5% to 0.25% in 2016.
The average easy access savings account on the market paid 0.54% just before the Bank of England base rate was cut from 0.5% to 0.25% in 2016, but more recently it has fallen to just under 0.4%.
As well as the low base rate, schemes such as funding for lending have been blamed in recent years for depressing savings rates further, as banks have been less reliant on needing to attract savers' cash with attractive rates.
Charlotte Nelson, a finance expert at Moneyfacts, said: "Today's rate decision may see some savers jump for joy, as it marks the first positive base rate move in more than 10 years.
"However, savers may want to hold back on the celebration, since the link between base rate and savings rates seems to be severed.
"Savers have struggled to find a decent return with rates at rock-bottom. For example, the average easy access account stands at 0.39% today, while back in July 2007 (the last time base rate rose) it stood at a whopping 4.05%.
"Savings rates have finally taken a positive turn over the past year, with challenger banks stepping in to offer savers some sort of return.
"As a result, the average two-year fixed rate has risen from 1.09% a year ago to 1.44% today."
Martin Lewis, founder of MoneySavingExpert.com said: "Low interest rates have been a plague for many with savings, especially those who retired and expected to live off the interest."
He said: "Many people have money in savings accounts already paying pitiful, spit-worth rates like 0.1%, and they are unlikely to rise.
"Those in a middling account paying about 0.5% may see an increase over the next few weeks."
Mr Lewis suggested savers earning less than 1% interest "should ditch and switch".
The base rate increase is also expected to provide a modest boost for pensions.
Former pensions minister Sir Steve Webb, who is now director of policy at Royal London, said: "After a decade of low and falling interest rates, today's rise provides a modest boost for pensions.
"If today marks a turning point in interest rates this should signal a gradual recovery in annuity rates and could help to reduce deficits in company pension schemes."