Did the Sea Vixen ever realistically operate on DLI?
That's a very good question. The most logical explanation I can come up with is that need to consider the dates - the navy started looking towards a new aircraft in 1946, the specification was issued in 1947, it first flew in 1951 and considering how short development periods were then and for the aircraft of the period that had just preceded it they must have been expecting it to enter service a couple of years after that at most in say 1953. This was all, especially the initial work and specification, well before aircraft like the Canberra or B-52 had entered the picture so they probably weren't expecting opposition that could later fly so fast or so high. When the Soviets start test flying and then introducing aircraft like the Tupolev Tu-16 Badger and Tu-95 Bear in their naval aviation units whose increased speed and service ceilings starts drastically cutting into the time defending aircraft have to get up to height and out to meet them far enough away from the carrier and accompanying ships they've got a problem. Same goes for aircraft stationed in a country that shares a border with an unfriendly neighbour such as West Germany where you can have limited response time from when enemy aircraft can be picked up on radar and crossing the border.
This then prompts people to start looking at combined jet- and rocket-powered interceptors like the SR.53 and later SR.177 since we're still in the early to mid stages of jet development and afterburner/reheat equipped engines weren't really there yet. In the meantime the Sea Vixen takes an age and a day to finally enter service by which time it's already starting to become obsolete, but because of all the money sunk into it and that it's the only real domestically built option just have to take it. Reheat by this point has been perfected, jet engines have become more powerful and fuel efficient, and aircraft such as the F-4 were taking their first flight only a year after the SR.177s. This allows you to do things like mount a standing CAP with aircraft that have a very good turn of speed, will already be at height and have a much more developed radar. On the RAF side of things they've already buggered off with the English Electric Lightning. It all
seems to hang together and in the typical slightly screwed-up British military procurement mysteries manner, whether it's correct or not sue to unseen variables I can't say for sure.