sunak has zero control over interest rates, (or inflation) but hes said specifically he will bring inflation down.

Not quite. Inflation can be caused from the supply side, and from the demand side. While inflation caused by the demand side (covid stimulus) could only be addressed by BoE rates, the inflation caused by supply side (covid disruptions in supply chain, followed by Russia → Ukraine war hitting energy prices, and continuous problems arising from brexit) is something that he could influence.

So, to sum it up, he has partial influence over the inflation, and in addition to what he could control about the supply side of inflation, he was betting that BoE would be doing a better job controlling the demand side of inflation.