Monetary Policy Committee members predict any rise in the Bank base rate, currently at 0.5%, which occurs over the next two to three years will be gradual.
And the base rate is likely to remain below the 5% average set by the committee before the financial crisis, the minutes from February's MPC meeting have shown.
The level of quantitative easing, the stock of purchased assets, will remain at £375bn at least until the first rise in the base rate.
Members thought that inflation, which fell back to the target of 2% in December, was likely to remain at that level with the probability of it rising to or going above 2.5% in 18 to 24 months around one third.
This month, inflation dropped below the Bank's 2% target to 1.9%.
Members said the recent unexpectedly sharp falls in inflation reflected underlying cost and price pressures that were weaker than currently judged.
Inflation would continue to be sensitive to developments in commodity prices and the exchange rate, both of which could move sharply.
The Bank of England's estimates for growth were a little under 1% per quarter in the first two quarters of 2014.
The unemployment rate had fallen to 7.1% in the three months to November and data to be released in the next few months is likely to show it reaching the Committee's 7% threshold.
The minutes stated: "There was therefore no reason to alter the Committee's judgement that medium-term inflation expectations remained sufficiently well anchored."
Members voted unanimously to maintain the base rate at 0.5% and QE at its current level of £375bn in February.