Four out of 10 savers do not think it is worth switching because they assume all providers pay broadly similar rates.
Yet while almost two thirds of savers who last transferred account in 2005 or earlier get 0.1% interest or less before tax, they could earn almost six times the Bank of England base rate in an easy access account or nine and half times by fixing for five years (see the Top Savings Accounts guide).
Meanwhile, millions who opened an account over a year ago should also beware plummeting rates given most best-buy accounts have for the past few years added bonuses to boost the rate, which tend to expire after 12 months.
In particular, we warn today in our weekly money tips email that savers who took out the top accounts a year ago from the AA, Coventry Building Society, Santander and Ulster Bank should switch soon due to plunging returns.
Yet 40% of savers are still loathe to switch, according to research by consumer group Which?.
It found roughly 87% of accounts around in 2005 currently pay pre-tax returns of up to only 0.5%, while 62% pay 0.1% or lower.
Despite the low returns on offer, 35% of savers admit they have money sleeping in accounts they opened at least six years ago.
A basic rate taxpayer would earn just 8p per year in an account paying a pre-tax 0.1% for every £100 held, compared with £2.32 if they opted for a best buy easy access account paying returns of 2.9% before tax. This compares to the current historic low base rate of 0.5%.
That 2.9% deal is available from the Post Office, but it includes a year's bonus of 1.25%.
Meanwhile, if you're prepared to lock your cash away for the term you can get a fixed 3.25% before tax for one year from Firstsave, 3.15% for two years from Northern Rock or 4.75% for five years from Coventry BS.
Which? chief executive Peter Vicary-Smith says: "All too often, banks and building societies lure in savers with attractive rates of interest, then reward their loyalty by quietly slashing rates to a paltry level later on.
"It's a scandal that banks seem to reserve the most pitiful returns for their most loyal customers."
Additional reporting by the Press Association.
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