The big difference between the Fed and the UK/EU banks is their remit. The UK/EU bank rates are set, specifically in the UK and generally in the EU, to target INFLATION. The Feds remit is to ensure GROWTH. With this fundamental disparity the US interest rate, and hence the currency will generally be below the £ or Euro.
In my time the HK$ has varied between 8.8 and nearly 16 to the £.........