Those in the first part of your list are also described as E-3D, RC-135, CH-47, C-130J, P-8. The three of those in bold are used much more widely than their British names within the RAF at large. And the Airseeker is called a Rivet Joint by everyone I’ve ever talked to (admittedly none from 51 Sqn though). I don’t think there’s any rhyme or reason to it.
On F-35, can you imagine the confusion if the UK called the B “Mk1” and maybe later the A “Mk2”? Thankfully we don’t seem to have adopted that either!