The move comes as Sainsbury is poised to announce further details of its new telephone banking operation, the latest in a series of forays by retailers into the banking arena.
The TSB Select account - which customers must pay a fee of pounds 3 a month to join - offers a hotline that will enable members to find the best price on more than 25,000 items including hi-fis, fridges and washing machines.
As there is no catalogue customers must decide broadly which product they want before contacting the hotline. The deals offered include those from manufacturers selling direct. The prices are compiled through database operator CUC Europe.
"Prices will be significantly cheaper than those available on the high street," claimed Peter McNamara, TSB's managing director of current accounts.
TSB says it will make no margin on the sale of products but hopes to gain revenue through credit card transactions and finance deals. The account also offers a motoring service where customers receive a guaranteed pounds 500 off a new car.
Rivals said service was unlikely to work. "We considered this idea but didn't feel it had sufficient appeal," said Gordon Rankin, head of personal banking at Barclays.
He said TSB's idea was simply another example of "charged for" bank accounts.
Barclays launched Barclays Additions in October where account-holders also pay a monthly fee. NatWest has since launched NatWest Premier.
Mr Rankin said the flurry of launches would help establish the market for bank accounts where customers pay a monthly fee for a premium service. "The old method of having one kind of account for all customers is gradually giving way as people seek more choices."
TSB claims that customers will recoup their pounds 3 a month charge if they make two purchases yearly.