It was inferred by a previous poster that the military would not be subordinate to the police in a disaster as depicted in the film. In fact the military role would be to supply aid to the civil authorities when requested to do so. The civil authorities would retain primacy. In practise the Army would need 48 hours or so to mobilise themselves, there not being much Army presence in London, especially with current overseas commitments. Even then they would be dependent on calling in the TA.
As for COBRA, we were given the impression that it was a full governmental emergency department in its own right - even reference to a Met Police Cobra Division. In fact COBRA stands for Cabinet Office Briefing Room "A". It's just the room where the PM or DPM meet their advisers to discuss the current emergency!