The bank said it had sold $37.6 million at a cut-off price of 7.1401 pounds per dollar, unchanged from the previous sale on Wednesday.
The rates at which banks are allowed to trade dollars are determined by the results of central bank sales, giving the bank effective control over official exchange rates. The bank offered $40 million on Monday.
In the unofficial market, the pound was trading at 7.50 to the dollar at midday, one trader said, also unchanged from earlier in the week.
The rate for dollar sales has kept within a tight range since the beginning of June after the bank allowed the pound to weaken in May.