The decision to keep interest rates on hold for now will bring "scant relief" for savers, experts have said.
The average easy access Isa rate on the market has already dipped below 1%, according to financial information website Moneyfacts.co.uk.
Meanwhile, mortgage lenders have been offering some of their lowest rates ever.
Calum Bennie, a savings expert at Scottish Friendly, said: "The decision by the Bank of England Monetary Policy Committee not to cut the base interest rate beyond its already historic low will come as scant relief for cash savers.
"Savers have been waiting patiently for rates to go up and as the UK economy improved all signs were that Carney and co were creeping towards an increase in the not too distant future. However, with the economic uncertainty unleashed around Brexit, all such bets are now off."
But Yvonne Braun, director of long-term savings and protection policy at the Association of British Insurers (ABI), said those considering buying a retirement income called an annuity with their pension savings would welcome the Bank's latest decision.
She said: "Savers and customers considering buying an annuity will welcome the decision by the Bank of England not to further ease monetary policy today.
"Sustained quantitative easing combined with continued low interest rates is one of the main factors keeping annuity rates low and further action by the Bank of England could have added to the downward pressure."
Mark Harris, chief executive of mortgage broker SPF Private Clients, said it was still "highly likely" that a rate cut could come in August.
He said: "Lenders are already factoring a rate cut into their pricing, with Santander increasing the premiums over base rate on some new products to protect its margins in readiness of a rate cut."
According to calculations from the Council of Mortgage Lenders (CML), a quarter point fall in the base rate, if passed on fully to someone's mortgage costs, could shave around £26 a month off someone's mortgage payments, assuming they were on a 25-year repayment term and had borrowed £200,000.
The extent to which borrowers could expect to see a change in their mortgage costs when the base rate does eventually change depends on whether their deal is directly tied to the base rate.
Some variable rate deals specifically track the bank rate. But others do not - and for these deals changes in the variable rate would be up to the individual lender, as the bank rate is just one of the factors lenders take into account when setting mortgage rates.
The CML's estimates suggest around 1.5 million existing mortgages are bank rate trackers. In general, the rates on these deals track the movements of the base rate, plus a certain percentage margin specified by the lender.
According to the CML, around half of all existing mortgage holders across the UK are on fixed rates and half are on some form of variable rate deal.
Rachel Springall, a spokeswoman for Moneyfacts said she had seen some "best buy" savings deals withdrawn from the market entirely in recent days.
Since January, around nine cuts have been made in the savings market for every single increase. More than 900 individual cuts to savings rates have been made since the start of 2016, while just over 100 rate increases have taken place over the same period, according to Moneyfacts' data.
Ms Springall said the average rate on offer on a two-year fixed bond has fallen from 3.34% in 2009 to 1.75% a year ago to just 1.39% in July. The average easy access Isa paid 1.31% in 2009 and had fallen to 1.12% a year ago - and now pays 0.98% typically.