"The link between the bank base rate and savings has been severed for years, most recently thanks to government lending initiatives, which has meant banks don't need savers' cash to fund their mortgage books as they used to", explains Rachell Springall of Moneyfacts.
Baroness Altmann said: 'Banks are very quick to pass on any savings cuts and then they don't pass on the increases.
And he emphasised that despite the significance of the first rise in rates for a decade, a low interest rate environment still prevailed. Gammon pointed out that interest rates are still historically low.
"Looking forward, the MPC has made it clear that any further rises in interest rates will take place at a gradual pace".
"The 0.25% lift in the base rate will likely be passed on to borrowers on variable-rate mortgage deals nearly immediately-with a material effect", said Simon Gammon, managing partner at Knight Frank Finance.
But it will offer some relief to savers hit by surging inflation and negligible returns.
But analysts warned the Bank's suggestion that Thursday's rise will not be a one-off event and that further hikes over the next three years could hit thousands now on variable rate mortgages.
"The time has come to ease our foot a little off the accelerator", Bank governor Mark Carney said.
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%.
But sterling fell sharply, down more than 1% to $1.31 and €1.12, as the Bank's comments over future rises were more cautious than expected.
It is pencilling in growth of 1.7% for 2020.
By that measure, a homeowner with a £1 million (US$1.03 million) variable-rate mortgage would be paying an extra £208 (US$272) every month as a result of the rate hike. Mr.
Yesterday, Virgin announced increases of 0.25 percentage points to selected savings accounts with no change to mortgage rates.
"The increase has no bearing on those borrowers who have fixed rate mortgages, which accounts for the vast majority of customers we have lent to in the last five years since re-entering the market".
The Bank of England's Monetary Policy Committee voted to move rates up after 10 years amid "headwinds" in the British economy.