I'm sure someone else can do a much, much better explanation than I can, but... As I understand it, it comes from the perception that inflation is driven by a "too much demand" problem (ie, too much money in the system chasing the same amount of goods), and by raising interest rates they discourage spending and encourage saving, both serving to reduce demand.

Obviously there are valid questions about whether raising interest rates to deal with a "not enough supply" problem actually helps or causes more harm - and given that the current inflation was initiated by Russia's invasion of Ukraine, which resulted in supply disruptions. The problem was not a surplus of money, but a deficit of goods. And, of course, a lot of things most hit by inflation are impossible to meaningfully reduce demand for, like food and electricity.

I have suspected for a while that raising interest rates to deal with inflation is largely a "when all you have is a hammer, everything looks like a nail" situation: the Bank of England only has one tool - changing interest rates - so when faced with a problem, the only thing they can do is raise or lower interest rates.