Fantastic post, thank you very much, I have been looking for information on UK INS procurement/development/licensing for years!
I have had a chance to visit the formerly Litton now NG subsidiary in Italy and was told how for the F-104 project they hired every watchmaker they could find and employed hundreds. MTBF was tens of hours at best but man-hours for production was thousands. A huge facility was constructed and today only a fraction of it is still used though INS are still manufactured there.
I know Sperry Gyroscopes (UK) flew a system designed for manned fighters in November 1954 (were not allowed to show it until 1958). EE were apparently working on their own gyros and platforms both prior to and after the Honeywell license (for miniature integrated gyroscopes) and SG Brown had the manned fighter contract with two gyro master reference units, the Mk 1 and 2 MRGs which were their own design (I believe?) but the Mk3 used the Arma brown floated Gyros- that may have been for helicopters, there was a Brown-Arma gyro compass for use in helicopters and Hovercraft- it was actually used in the Denny D2. Brown also did maritime INS though having been an admiralty holding until 1960. Then there was the Brown Gyrotwin that appeared in 1960 (though claimed to be all British).
Both EE and SG Brown got their license in the same year, 1958, so I have always assumed they were competing for something- Lightning perhaps? Equally, Sperry gyros flew its design in 1954 which was the same year SG Browns system first appeared so I always assumed some sort of competition there- Swift / Hunter / Scimitar possibly? Just a theory for which I have zero evidence.
As for the later versons (SG Brown/Bendix, Rank Cintel/GTI) I have no idea! Could have been speculative given continued avionics developments elsewhere? Elliots ultimately got Jaguar (E.3R- total nav/attack system package was NAVWASS) and Nimrod (E.3 platform). I understood the Tornado/TSR-2 link to be the following: the TSR-2 system was in some way adapted for the Harrier and that system was then further developed (becoming digital and first of the FIN.1100, as FIN.1010, family) for MRCA? I always assumed that the Harriers Ferranti FE.541 INAS (Kearfott derived gyros used in the Ferranti Miniature Inertial Platform) was what was meant as the definitive fit for the P.1154 (both were analogue) following the abandonment of the originally desired digital system? Ferranti FE.541 INAS became FIN.1065 when fitted with electronics from the FIN.1075 used in the GR.5 (modification made under RAE project Nightbird to upgrade T.4 to T.6 for GR.5 training), FIN.1075 was grossly unreliable and at least 32 Litton ASN-130s were acquired as a result. The original Jaguar system was replaced by the FIN.1064 which when rebadged for the Harrier became the FIN.1075. Nimrod MR2 got FIN.1012, FIN.1070 for EAP. Ferranti got to propose FIN.1063 in Buccaneer (FIN.1064 with weapons aiming circuitry redundant) with 60 units planned. FIN.1040 was exported to Japan for the Mitsubishi F.1. All from the FIN.1100 family.
Also, let us not forget civil aircraft, Elliots at least prototyped an INS for airliners and it was test flown on a BOAC 707, pre-production models called E.3 and E.5, the latter was marketed but I dont know how successfully. There was also an E.4 unit marketed at some point. I doubt they sold much, even VC-10's got the Delco Carousel systems- which later got shoe-horned into Vulcans for Black Buck.
Ferranti, IIRC, got Concorde prototype (production aircraft used the Ferranti-SAGEM SF 500-AESI). Phantom F-4M, in addition to the Harrier, used the miniature inertial platform which also made an appearance in ELDO and Black Arrow. A digital version was being touted in 1972 and was being referred to as Dins for awhile, probably forms part of the family tree to FIN.1100. Miniature Inertial Inertial Platform was more popular than NAVWASS as it was all in one box.
In a lot of cases UK companies only licensed the Gyros (admittedly a vital part of the system) not the entire INS for which they did a lot of their own work.