Yes, this is a Mil crosser. At several points in UK airspace there are corridors that are used to cross Military traffic through civil airspace. The Mil Controller will coordinate a level and will transit the airspace. They are not transferred to the civil controller. Your job is to keep your traffic 1000 and 3 or 5 nm (depending on your sector) separated from it.
I always ‘point out’ the traffic and once clear if your airspace, ‘drop’ it. If possible look at the route, as it might return if it is a Round Robin flight. I am not sure it would be coordinated a second time.
Cheers, C
Ps. If you ever have these type of flights that are not coordinated, please report them in a separate post.