The nine-member Monetary Policy Committee (MPC) of the Bank of England (BoE) voted unanimously on the holding of benchmark interest rate and quantitative easing policy this month, according to the central bank's meeting minutes published on Wednesday.
But two members reckoned that it is "finely balanced" between voting to hold or raise the rate.
The British central bank announced on May 11 that Bank Rate would stay at 0.5 percent and the stock of asset purchases, or quantitative easing policy, maintain at 375 billion pounds (or 580 billion U.S. dollars).
The MPC noted the policy trade-off that had appeared over the past months: inflation remained below the target while unemployment was still somewhat above its long-run sustainable rate.
"Eliminating the remaining economic slack, and so returning output to its sustainable level, should reduce the drag on domestic costs and prices, helping to return inflation to the target," the minutes said.
Britain's Consumer Prices Index (CPI) fell by 0.1 percent in the year to April 2015, it is the first time that CPI has fallen over the year since official records began in 1996 and the first time since 1960 based on comparable historic estimates.
However, British unemployment rate fell to 5.5 percent in the three months to March 2015, lower than the 5.6 percent of the three months to February 2015, recording the lowest level since mid 2008.
But the committee believed that in the absence of further falls in energy prices or sharp movements in the exchange rate, inflation rates close to zero would be unlikely to endure for very long.
"As the impact of past movements in energy prices and exchanges rate faded from the 12-month calculation, CPI inflation was likely to rise notably towards the end of the year," it noted.