I dont see the big fuss.
We Limeys used to kill British citizens (members of the IRA and INLA). If we could arrest them, great. If we had to kill them, so be it.
You turn against your country and attempt to harm it, you pay the consequences of your violent actions.
Well.. here we have due process. Who and what determines the purported "violent actions" and the guilt of the accused? I don't pretend to know the methodologies as to how the Brit government concludes who's a legitimate target, but over here those details need to be fleshed out. The idea of any president playing the role of judge, jury and executioner tends to rub us Americans the wrong way.