The Bank of England has reiterated it is in no rush to raise rates, with governor Mark Carney saying they may remain low "for some time".
Nevertheless, the economy has "edged closer" to the point where interest rates would need to rise, he said.
The comments led to a fall in the value of the pound against other currencies.
There has been market speculation that interest rates will rise before the second quarter of next year, when a general election is due to be held.
Mr Carney said any increases in interest rates would be "gradual" and that rates "may stay at historically low levels for some time".
Some analysts had thought the recent strength of the UK economy might force the Bank to raise rates before the second quarter of next year, but this now appears less likely.
Following Mr Carney's comments the pound was down 0.3% against the dollar at $1.6778 and dropped 0.35% against the euro to 1.2236 euros.
In a report on Wednesday, the Bank of England upgraded its growth forecasts for next year, saying the economy "has started to head back towards normal".
Its latest inflation report predicts growth of 2.9% next year, up from its 2.7% forecast three months ago.
Although the Bank raised its growth forecast for next year, it left its prediction for this year unchanged at 3.4% and trimmed its growth forecast for 2016 to 2.8% from 2.9%.
"Securing the recovery is like making it through the qualifying rounds of the World Cup - it's a real achievement, but not the end goal. The prize in the economy is sustained and prolonged growth," Mr Carney said.
The Bank has also sharply upgraded its forecasts on unemployment. It now predicts the unemployment rate will fall to 5.9% in two years, compared with its prediction last year that the rate would remain above 7% for some years.
The forecast upgrade followed the latest official jobs data showing the unemployment rate was 6.8% in the three months to March.
The Bank also said there was still a significant amount of "slack" in the economy, meaning that it was not growing to its full potential because of underinvestment.
It noted that both employment levels and average hours worked were still both below pre-crisis levels.
In February, the Bank estimated that the spare capacity was equivalent to 1% to 1.5% of gross domestic product (GDP).
The Bank said there had been a "modest fall" since then, but did not give an exact figure.
"The path of slack is uncertain, and there is a range of views on the [Monetary Policy] Committee. For a given growth profile, it will depend heavily on the timing and strength of the rebound in productivity growth," the Bank said in its report.
The Bank said it also expected inflation to remain below its 2% target in two years' time.
Capital Economics economist Samuel Tombs said he expected the inflation report to "go some way to cool expectations that the Monetary Policy Committee will raise interest rates as soon as the first quarter of next year".
"We continue to think that interest rates will remain on hold until the second half of next year, later than the markets and most economists expect," he added.