The central bank has kept the official exchange rate steady for more than two months after letting the pound weaken at the start of the year, which, combined with other measures, has seen black market trading almost disappear.
The bank said it offered $40 million at auction on Wednesday and sold $38.4 million at a cut-off price of 7.5301 pounds per dollar, unchanged from its last auction on Thursday before a long holiday weekend.
The rates at which banks are allowed to trade dollars are determined by the results of official auctions, giving the central bank effective control over exchange rates.
One trader in the parallel market said the pound was trading at 7.65 pounds to the dollar on Wednesday, the same rate quoted following the last official auction on Thursday.
Black market traders say volumes have fallen dramatically since the central bank's move against them and since it imposed a cap in February on the amount of dollars that can be deposited in banks.
The limit discourages use of the black market by depriving those who exchange dollars outside official channels from a place to keep their funds.