The Bank has cut rates three times in the past seven meetings
Some members of the Bank of England's Monetary Policy Committee considered raising rates to curb inflation at its June meeting, minutes have shown.
However, the MPC decided an unexpected rise might have exaggerated the level of its concerns about the outlook for inflation, the minutes said.
Following its discussions, the committee voted 8-1 in favour of keeping interest rates at 5% in June.
One member, David Blanchflower, voted to reduce rates to 4.75%.
The committee voted to keep rates on hold for the second month in a row in June after a number of cuts since December last year.
On Tuesday, government figures showed that consumer inflation rose at an annual rate of 3.3%, the fastest rate since the Consumer Prices Index began in 1997.
The MPC said that led it to believe that inflation would rise by more than expected in the medium term.
"For some members, the news had been sufficient to consider whether an immediate rise in Bank Rate was warranted," the minutes said.
Although the prospect of higher rates was dismissed, "the fact that the case for a rate hike was even discussed will keep the markets nerves jangling", said Jonathan Loynes from Capital Economics.
Other economists perceived last month's meeting as a turning point and predicted some members would soon vote for a rise.
"I think it may not be long before we see a three-way split on the committee," said George Buckley from Deutsche Bank.
"In such a scenario, the bulk of votes are still likely to be for no change," he said.