The nine-strong panel which sets interest rates, called the Monetary Policy Committee (MPC), justified the rate increase by saying that falling unemployment means there is “limited” slack in the economy.
Seven out of the nine members voted in favour of higher rates.
They believe that growth cannot accelerate much more without causing prices to rise more quickly.
However, the MPC repeated previous guidance that future increases in rates would be at “a gradual pace and to a limited extent”.
The financial markets are indicating two more interest rate increases over the next three years, taking the official rate to 1%.
The MPC also said that the decision to leave the European Union is having a “noticeable impact” on the economic outlook.
It said there were “Brexit-related constraints” on investment and labour supply, which were holding back the potential growth rate of the UK economy.
The Bank of England, under the leadership of governor Mark Carney, is tasked with keeping consumer price inflation at around 2%.
However, inflation has been running higher than that since February, and in September it hit 3% – the highest rate since April 2012.
The Bank thinks that inflation is likely to peak this month at 3.2%.
Despite accelerating inflation, the Bank has been reluctant to raise interest rates.
It has argued that inflation has been boosted by the fall in value of the pound since the UK’s vote to leave the European Union in June of last year.
That weaker pound has driven up the costs of imported food, fuel and other goods. The Bank says this effect is probably at its peak at the moment.
The other issue holding back the Bank has been the weakness in wage growth. While inflation hit 3% in September, wage growth was only 2.1%.
However the Bank sees wage growth “gradually” increasing over the 2018 and says there are signs of that happening already.
In its Quarterly Inflation Report, released with the announcement on rates, the Bank slightly raised its growth forecast for this year to 1.5% from 1.3% and also edged up its growth forecast for next year.