Now show the UK plot for the 2010s. Also, show the one for Japan. It's easy to cherry pick data to show whatever you want. It doesn't constitute strong data for a casual and reliable link between interest rates and inflation.
Plot the days when your air conditioner is on with the temperature of your room. It will have many concrete examples and a long-term correlation showing that actually, the air conditioner is associated with the temperature going up.
All feedback/control systems are like that.
Your argument would have more weight if the inflation predictions were accurate. Here's the prediction report for the BoE in Aug 2014: https://www.bankofengland.co.uk/-/media/boe/files/inflation-...
(It's worth noting that even with the assumption of the models used being useful, the spread on those inflation rates is wild).
Here's what actually happened: https://www.ons.gov.uk/economy/inflationandpriceindices/time...
It very rapidly hit the bottom end of the prediction range before jumping up again pretty high. All that time interest rates were held constant and low.
Given they claim feedback lags of two years or so, one wonders what the point of all this is... (one cannot run a control loop with control lags substantially longer than the time constant of the system; that's basically the recipe for an unstable control system, assuming of course the control system is doing anything).
There's an argument that it's inflation expectations that matter, but there are dissenters within the temple that disagree: https://www.federalreserve.gov/econres/feds/files/2021062pap...
The second link https://www.macrotrends.net/global-metrics/countries/gbr/uni... is from 1960 to 2023.