The central bank said it sold $37.6 million at a cut-off price of 7.1401 pounds per dollar, unchanged from its last sale on Wednesday.
The rate for the dollar sales has stayed within a very tight range since the beginning of June, after the bank allowed the pound to weaken in May. It had offered $40 million on Wednesday.
On the black market, the dollar changed hands for 7.39 pounds, one trader said, weaker than the rate of 7.385 on Wednesday.
The rates at which banks are allowed to trade dollars are determined by the results of the central bank sales, giving the bank effective control over official exchange rates.