But he warned: "We need to make sure inflation stays low and be careful not to cut interest rates too quickly or by too much."
The Bank also considers other measures of inflation when deciding how to change rates, and some of these remain higher than it would like.
Some parts of the economy, like the services sector - which includes everything from restaurants to hairdressers - were still seeing more significant price rises in recent months.
It has to balance the need to slow price rises against the risk of damaging the economy, and avoid cutting rates only to have to raise them again shortly afterwards.
Although UK inflation briefly hit the Bank's 2% target in May and June, it is forecast to remain slightly above that level for the rest of 2024, before settling back down in early 2025.
So, it is difficult to predict exactly what will happen to interest rates.
In May, the International Monetary Fund (IMF) recommended that UK interest rates should fall to 3.5% by the end of 2025. The organisation, which advises its members on how to improve their economies, acknowledged that the Bank had to balance the risk of not cutting too quickly before inflation is under control.
More than half a million homeowners have a mortgage that "tracks" the Bank of England's rate.
But more than eight in 10 mortgage customers have fixed-rate deals. While their monthly payments aren't immediately affected, future deals are.
Mortgage rates are much higher than they have been for much of the past decade, with the average two-year fixed rate now at 5.47%, according to the financial information service Moneyfacts.
Mortgage lenders have been in intense competition for customers and have dropped their rates. But homebuyers and those remortgaging are still having to pay a lot more than if they had borrowed the same amount a few years ago.
About 1.6 million mortgage deals are expiring in 2024, according to banking trade body UK Finance.
You can see how your mortgage may be affected by interest rate changes by using our calculator:
Bank of England interest rates also influence the amount charged on credit cards, bank loans and car loans.
Lenders can decide to put their rates up if they expect higher interest rates from the Bank of England. However, if rates fall, interest payments may get cheaper.
Low interest rates are good for borrowers, but bad for savers [Getty Images]
Savings
The Bank of England interest rate also affects how much savers earn on their money.
Individual banks and building societies have been under pressure to pass on the recent higher interest rates to customers.
What is happening to interest rates in other countries?
In recent years, the UK has had one of the highest interest rates in the G7 - the group representing the world's seven largest so-called "advanced" economies.
In June, the European Central Bank (ECB) cut its main interest rate from an all-time high of 4% to 3.75%, the first drop in five years. It cut rates again to 3.5% in September.
The cut - the first in four years - was larger than many analysts had predicted, and the bank signalled that rates could fall by another half percentage point by the end of 2024.