Day, night, IMC, VMC, way out over La Manche, over Scotland, over or close to London? My point again is that no to two scenarios are the same. That's Air Defence in the modern era.
In the simplest scenario, the visual intercept signals work well and a Typhoon knocking on the window won't go unnoticed for long. An aircraft in distress might happily follow an interceptor to a nice safe runway. As conditions become more difficult, the decisions become more complex - way beyond the public forum, but not difficult to imagine.
But again, every scenario is different and decisions will always be made on the information available.
Some may say it ain't always perfect; I would certainly not subscribe to that publicly.