Inflation and a declining standard of living are two different things. Inflation is when the money becomes less valuable, resulting in rising prices. But when a whole society becomes poorer, it can look like inflation, because prices may rise, but it’s not the same thing.
“Despite the Bank of England’s efforts so far, there is accumulating evidence that inflation will be harder to stamp out than previously expected. In the past week, data has shown that pay in Britain has increased faster than expected, inflation in the services sector has accelerated and food inflation is still near the highest level in more than 45 years.”
https://www.nytimes.com/2023/06/22/business/economy/bank-of-england-interest-rates-inflation.html?smid=url-share
To my eye, viewed from over here, that looks less like inflation and more like a falling standard of living—largely caused by Brexit. If you block immigration, of course wages are going to go up. If transporting stuff across the border takes longer and is more expensive and difficult, of course food is going to be more expensive. That’s not inflation. That’s reducing everyone’s standard of living by raising actual costs.
It looks similar, because the symptom tends to be rising prices, but they’re two different things. If the problem is inflation, then raising interest rates (by reducing the rate of growth in the money supply) will probably help. But if the problem is a declining standard of living, then it’s probably not going to help. Higher interest rates will just be yet another expense (like border controls) that flow through to making everything cost more.