Taxi Driver
You are correct; the CAA will normally award the multi crew hours that you have gained from military service as long as you are able to demonstate them - in my case, send them my log book with 'highlighted' multi pilot sorties.
You would still require a TR on a stated multi pilot type though. Even if you operate the KA as multi crew, this will not suffice as the KA iS categorised as a Single PILOT type. They will award you the multi crew hours if you have them, but not the multi pilot type - so the KA alone will not unfreeze your ATPL.