The bank said the cut-off price at the auction was 6.5500 pounds to the dollar - a 0.3 percent fall from Sunday when the cut-off price was 6.5299 pounds.
The central bank said it had sold $74 million at the auction, less than the $75 million it had offered.
On the interbank market, the central bank limits trades to a 0.5 percent band above or below the weighted average of bids at the most recent currency auction.
The weighted average on Tuesday falled to 6.5827 pounds to the dollar from 6.5624 on Monday.