"It's likely over the course of the next year rates will go up. that's the most likely thing to happen", Mr Carney said in an interview with the BBC, the broadcaster said.
On growth, the BoE said "very little spare capacity remains in the economy", which grew only 0.1% in the first quarter, down from 0.4% in the fourth quarter of 2017, hampered by poor weather.
The Bank's forecasts are still based on financial market expectations for three rates rises over the next three years, with one seen later in 2018 followed by another in 2019 and one in 2020, to bring inflation back to the 2% target in two years.
The Bank of England (BoE) has downgraded its predictions for inflation and economic growth in Q2, as the prospects for the United Kingdom economy remain "clouded by Brexit uncertainty".
Practically, this largely involves the Bank adjusting interest rates to try and keep inflation at, or as close to, a target of 2%.
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He said the bank wanted to see a growth pick-up in coming months before raising borrowing costs. The Bank of England had upgraded its growth forecasts and in March two members of the MPC broke ranks and voted for an immediate rate rise.
"Swap rates have been significantly more volatile than the bank rate in recent years".
This underwhelming start to 2018 also saw the BoE make some revisions to its growth forecasts for the year, with the bank now expecting the United Kingdom economy to expand 1.4% in 2018, rather than the 1.8% growth it had forecast back in February. For the majority of members, an increase in Bank Rate was not required at this meeting.
That could leave the door open for a rate rise in August, when the BoE next updates its economic forecasts, or November.
"The committee's best collective judgment therefore remains that, were the economy to develop broadly in line with the May inflation report projections, an ongoing tightening of monetary policy over the forecast period would be appropriate to return inflation sustainably to its target". Surveys have suggested little rebound last month. The BoE said weaker inflation was due to a faster fading of the impact of sterling's plunge on import prices, and that domestic inflation pressures continued to rise.