As Tourist said, I think you are confusing the two requirements; although I don't think that Tourist explained it fully either! (Sorry Tourist!)
There are two requirements for ATPL issue. The first is the hours required in a multi pilot environment, the second is a Type Rating on a multi pilot aircraft.
If you can show the CAA that you have operated a type (any type) as multi pilot, they should award you the hours requirment - I managed to persuade them that my Gazelle hours count based on my logbook showing multi pilot operations. Where you will come unstuck is that the King Air is classed as a single pilot aircraft, so unless you get another TR on a Multi Pilot Aircraft, you won't be able to unfreeze your CPL on the King Air alone.
I had this very conversation with the CAA just over a year ago, and this information was correct then. I don't believe anything has changed since, but I stand to be corrected.
Edited to say that I don't believe that the Authority will accept instructional hours as multi pilot hours; they certainly didn't when I was doing my license stuff. As I said above though, as long as you can show that you have the required amount of hours in a multi pilot environment on any type, they should award you that part of the requirement.