Strategic vs Tactical Airlift
The definition of Strategic Airlift is basically the ability to move force and equipment between theaters of war. The Uk, being an island state, will (hopefully) always fight outside its borders, ie, in different theaters of war. Although the Air Power of a state is, as you said, a combination of its military and civilian capability, specialised and fast reaction airlift can and will always be vested with the military. Not many civilian pilots would like to fly into active battle zones, and not many operators would see their way clear to employ their aircraft within such conditions, UNLESS an official state of war exists, which will then give the state the right to use all resources. However, for a state of war to exist, one country must officially declare such a state. So, in the "modern" concepts of armed conflict (Irac being the most recent example), no formal state of war exists. However, Britain is involved as part of an international agreement. As such, the state cannot commandeer any civilian resources, and has to rely on its statutory military force capabilities.
That is why a military force will always require an inherent stategic airlift capability. And this would also be true for operational and tactical airlift, and the other elements of Air Power.
Hope this helps.