Having worked in Emergency Planning, it is probably worth pointing out that 'Major Incident' can mean different things to different organisations.
Typically, any agency/organisation can declare a 'Major Incident' within its own area. Exactly what that means can vary from organisation to organisation, but it roughly equates to the deployment of resources well in excess of the norm.
However, beyond that is the more formal declaration of a multi-agency Major Incident, which stretches the resources of several organisations, responding to a significant event.
For the public, I appreciate hearing the term 'Major Incident' can be somewhat confusing, but the organisations involved have well tried and tested escalation and co-ordination arrangements in place.
Oh, and if a 'Major Incident, is significant enough, in terms of resources involved and/or of national significance, then the government will get involved and you may hear reference to COBR (or Cobra as the media incorrectly refer to it), which stands for Cabinet Office Briefing Rooms. In reality, this is a Ministerial (often PM) led committee that looks at the very high level issues in respect of an incident.