First, Sunak sets interest rates. I know there is a pretence that the Bank of England does, but he can over-rule them. He might need to do so now.
Sunak/BoE sets short term interest rates. Short term nominal interest rates that is. The longer the term the more the market sets and not the BoE/Sunak.
However, matters get more complex. Because you cannot both have control of interest rates and also have control of the money supply. Because the way that you control the one is by the other. Therefore you can only set the one and have to adjust the other to reach that setting.
Which means that if you can only control, fully, one of the two then inflation is something you cannot control. Or, perhaps, you can control inflation but only by setting the money supply/interest rates to do so.
All of which in turn means that you don’t in fact control real interest rates, you control nominal ones.