You seem to have no clue how an integrated air defense system really works. When the Cuban missile crisis began in 1962, Civil Air Patrol cadet squadrons all across the state were inducted into the Air Observer Corps. We had to learn aircraft identification, reporting format and proper phraseology, altitude estimation, and rudimentary weather observation, and we stood assigned watches, mostly relief periods for adult observers for breaks and meals. We were students and had homework to do, so we weren't expected to stand full shifts except on weekends. We called in every aircraft we saw with type, altitude and direction of flight, which was kind of a joke most ot the time, as there wasn't much air traffic out here in the sticks. Mostly Pipers and Cessnas, but there was a nearby SAC low level navigation route and we got treated to the occasional B47, BUFF, or tanker.
Our calls went to a filter center that plotted the tracks and compared them with tracks on the repeaters that they had from air defense radars. Suspicious tracks were investigated by the Air National Guard's F89s. Woe betide any flock of bears that chose to trespass; those Scorpions toted nuclear tipped Genie missiles. Between the radar, the observer corps, and the Scorpions, our section of the northern border was locked down pretty tight.
Our effort was thrown together pretty quickly, so we barely got it figured out when Khrushchev blinked and the crisis was over. The Brits, OTOH, had plenty of time and plenty of practice and got really good at it.
One other point. In the Navy I maintained and ran a radar interception and tactics trainer for the F4, so I have a bit of an idea what it's about. If you wait til you know the target before you send your fighters up, you've already lost the battle. You meet them beyond the edge of your airspace and you peck away at them all the way to the target and back. If you're flying especially short ranged point defense interceptors you send them up in relays and you land them as transients at the nearest airstrip to refuel and rearm, then launch them again to tackle the bad guys as they're egressing after the raid. If their escorts are toting drop tanks, tackle them as far out as you can and make them drop their extra fuel. Now you may soon have unescorted bombers to pick on. Don't worry, you won't lose track of them after they've come past the radar; there'll be so much commotion going on overhead, people on the ground will keep you informed. That, my friend is how it was done.