<<McGee is an Irish/Scott name.>> Firstly, there is no such description as 'xxx/Scott' name. Do you mean Scot's or Scottish by any chance?

<<I would be suprised if it was in any English listing >>
Who said that it was searched for '...in any English listing'?
When something is referred to as British without any further adjective involved, it usually pertains to the British Isles which consists of England, Ireland (including Eire), Wales and Scotland.

Like McGee and Zocchi, there are no Kidrick entries in BRITISH armory.
Likewise, there are no continental European (which is also France, Germany and the Germanic states, Poland, Hungary, Austria, Italy, Spain, Portugal, Norway, Sweden, Russia and the Russian States, Latvia, Lithuania, Holland, Denmark, Belgium, Luxembourg, Malta, Cyprus, San Merino, Andorra, Monaco, Greece, and also, I believe, the Vatican State) arms registered in the names of :
Kidrick, McGee, MacGee, or Zocchi.
The closest one to the Zocchi name is Zochowski from Poland.

Rgds,